Analytical Decomposition Research Articles

Vertical Velocity Dynamics in the North Atlantic and Implications for AMOC

Abstract The Atlantic meridional overturning circulation (MOC) is traditionally monitored in terms of zonally integrated transport either in depth space or in density space. While this view has the advantage of simplicity, it obscures the rich and complex three-dimensional structure, so that the exact physics of the downwelling and upwelling branch remains poorly understood. The near-equivalence of the depth- and density-space MOC in the subtropics suggests that vertical and diapycnal volumes transports are intimately coupled, whereas the divergence of these two metrics at higher latitudes indicates that any such coupling is neither instantaneous nor local. Previous work has characterized the surface buoyancy forcing and mixing processes which drive diapycnal volume transport. Here, we develop a new analytical decomposition of vertical volume transport based on the vorticity budget. We show that most terms can be estimated from observations and provide additional insights from a high-resolution numerical simulation of the North Atlantic. Our analysis highlights the roles of 1) relative vorticity advection for the sinking of overflow water at the northern subpolar North Atlantic boundaries and 2) the geostrophic β effect for the sinking of dense waters in the intergyre region. These results provide insights into the coupling between density- and depth-space overturning circulations. Significance Statement The purpose of this study is to better understand where and why dense water sinks in the North Atlantic. This is important because dense water sinking in the North Atlantic is a crucial component of the global thermohaline circulation. Our results reveal the primary controls on dense water sinking at a regional level and highlight the importance of mesoscale processes at high latitudes in shaping the circulation and heat distribution throughout the Atlantic Ocean.

Evolutionary diversity impacts tropical forest biomass and productivity through disturbance‐mediated ecological pathways

Abstract Significant research efforts have been made to uncover links between biodiversity and biomass productivity in forest ecosystems. However, the causal link between these two ecosystem components, and the underlying mediation role of disturbance, are yet poorly understood for hyper‐diverse tropical forests, because multiple ecological mechanisms are sequentially or simultaneously in play, leading to contradictory results in observational studies. Here, we introduce a novel framework for inferring the expected effects of evolutionary diversity on biomass stocks and productivity within forest ecosystems using observational field data. This framework involves an analytical decomposition of stand biomass into three key components: the number of trees, the mean size of trees and the mean wood density. Through this approach, we can distinguish structure‐ and compositional‐based diversity effects, which likely have distinct ecological origins. We tested this framework in one of the oldest tropical forest experiments, where different levels of silvicultural disturbances were applied in the 1980s, with regular monitoring since then. Our results revealed that disturbance history mediates the effect of evolutionary diversity on forest biomass dynamics and that several Biodiversity Ecosystem Function (BEF) relationships may be hidden behind the composite biomass variable. We specifically found an overall significant negative relationship between evolutionary diversity and biomass productivity soon after disturbances (~5–8 years), mostly via mean tree size, despite a positive evolutionary diversity effect on mean wood density. This result reflects that the productivity of disturbed forests is driven by a few dominant and disturbance‐prone species with low wood density and large potential stature, and not by niche complementarity among species. However, these effects rapidly vanished with time, with non‐significant overall effect of evolutionary diversity on productivity both ~30 years after disturbance and in the undisturbed plots. Synthesis. By disentangling the effects of evolutionary diversity on the different components of forest biomass, our framework unveiled how evolutionary diversity impacts forest productivity through different ecological mechanisms, and suggests that it plays a major role, albeit mainly negative, only soon after a disturbance.

Scattering matrices of particle ensembles analytically decomposed into pure Mueller matrices

Scattering matrices of particle ensembles are analytically decomposed into sums of pure Mueller matrices. The ensembles are assumed to have equal numbers of particles and their mirror particles, both in random orientation. In the general case, there are four pure Mueller matrices in the decomposition. In the present spectral decomposition, of these four matrices, there is a single matrix that qualifies as a scattering matrix, whereas the remaining three matrices represent other classes of pure matrices. For ensembles of spherical particles, there are two pure Mueller matrices in the decomposition. Again, there is a single matrix qualifying as a scattering matrix. The analytical decomposition unveils the explicit dependencies of the pure Mueller matrices on the ensemble-averaged scattering matrix. Applications are identified in scattering by single particles and by random media of particles.

The Systemic Governance Influence of Expectation Documents: Evidence from a Universal Owner

Abstract We examine expectation documents’ effectiveness as an activism tool. We use the Norwegian sovereign wealth fund’s release of a corporate governance expectation document as a natural experiment. We introduce a novel, three-way analytical decomposition of the firms, the fund, and their joint response to this document. Firms’ governance practices adapt to the fund’s new portfolio-wide governance preferences, with heterogeneous responses across ownership and firm characteristics. The fund’s investment policies also change, even at the expense of financial returns. Overall, our research demonstrates the potential effectiveness of expectation documents as an emerging, low-cost activism tool for universal investors. (JEL F30, G32, G34)

Monitoring-based identification of nonlinear aerodynamic damping in multi-mode vortex-induced vibrations of a stay cable

New issues of wind-induced cable vibration, i.e., multi-mode vibrations, increasingly occur in long-span bridges, which are closely associated with underlying damping features. In this study, an analytical method is proposed to identify nonlinear aerodynamic damping in multi-mode wind-induced cable vibrations in fields, involving the assessment of total and mechanical damping. The method is available to extract a series of mono-component resonances/decays from the measured signals based on the analytical mode decomposition (AMD) and random decrement technique (RDT), and then to determine the damping parameters using the Hilbert transform (HT) combined with the smoothing spline or linear least-square fitting. Furthermore, this method is applied to address the vortex-induced vibrations (VIV) of an ultra-long stay cable on the Sutong Bridge. Firstly, the vibrations are reported in terms of a typical event and one-year statistics. Subsequently, the damping parameters are identified to illustrate the in-situ aeroelasticity. The results show that the cable exhibits high-frequency vibrations primarily in the 41st to 43rd modes, and the aerodynamic damping exhibits significant amplitude-dependent nonlinearity. Finally, the damping identifications are employed to reveal the onset mechanism for the vibrations, and a Scruton number (Sc) criterion, i.e., Sc > 5.4, is suggested for mitigating the vibrations.

EiDA: A lossless approach for dynamic functional connectivity; application to fMRI data of a model of ageing

Abstract Dynamic Functional Connectivity (dFC) is the study of the dynamic patterns of interaction that characterise brain function. Numerous numerical methods are available to compute and analyse dFC from high-dimensional data. In fMRI, a number of them rely on the computation of the instantaneous Phase Alignment (iPA) matrix (also known as instantaneous Phase Locking). Their limitations are the high computational cost and the concomitant need to introduce approximations with ensuing information loss. Here, we introduce the analytical decomposition of the iPA. This has two advantages. Firstly, we achieve an up to 1000-fold reduction in computing time without information loss. Secondly, we can formally introduce two alternative approaches to the analysis of the resulting time-varying instantaneous connectivity patterns, Discrete and Continuous EiDA (Eigenvector Dynamic Analysis), and a related set of metrics to quantify the total amount of instantaneous connectivity, drawn from dynamical systems and information theory. We applied EiDA to a dataset from 48 rats that underwent functional magnetic resonance imaging (fMRI) at four stages during a longitudinal study of ageing. Using EiDA, we found that the metrics we introduce provided robust markers of ageing with decreases in total connectivity and metastability, and an increase in informational complexity over the life span. This suggests that ageing reduces the available functional repertoire that is postulated to support cognitive functions and overt behaviours, slows down the exploration of this reduced repertoire, and decreases the coherence of its structure. In summary, EiDA is a method to extract lossless connectivity information that requires significantly less computational time, and provides robust and analytically principled metrics for brain dynamics. These metrics are interpretable and promising for studies on neurodevelopmental and neurodegenerative disorders.

Near-critical behavior of the Zhong-Zhang model.

The Zhong-Zhang (ZZ) model is a one-degree-of-freedom dynamical system describing the motion of an insulating plate of length d floating on the upper surface of a convecting fluid, with locking at the boundaries. In the absence of noise, the system away from the boundaries is described by linear differential equationswith a delay time τ. The d,τ plane consists of two domains separated by a critical curve. For asymptotically long times, subcritical orbits approach a nontrivial periodic attractor, while the supercritical ones tend to a stationary state at the origin. We investigate near-critical behavior using a modified fourth-order Runge-Kutta integration scheme. We then construct a piecewise analytic decomposition of the periodic attractor, which makes possible a far higher level of accuracy. Our results provide solid evidence for an asymptotic power-law approach to criticality of several observables. The power laws are fed back to determine the piecewise-analytic structure deep into the near-critical regime. In an Appendix, we explore the effect of introducing noise using modified order-3/2 Kloeden-Platen-Schurz stochastic integration, following several observable quantities through the near-critical parameter domain.

SOFTWARE IMPLEMENTATION OF DECOMPOSITION METHODS FOR DETERMINING COMPLEX ONE-PARAMETER GENERALIZED INVERSE MOORE-PENROSE MATRICES (I)

Software implementations of analytical and numerical-analytical decomposition methods for determining complex one-parameter generalized inverse Moore-Penrose mat-rices are presented. Analytical methods are based on the first two Moore-Penrose con-ditions: in both cases the same solution to the problem is obtained, as it should be. Numerical-analytical methods are based on the obtained analytical relations and differential Pukhov transformations. Computational methods are implemented using modern infor-mation technologies, in particular Python programming language, NumPy and SymPy libraries. Software implementations consist of programs for entering the di-mensions and elements of a given matrix, implementation of an analytical method, de-termination of matrix elements derivatives and their values, calculation of matrix discretes and restoration of original matrices, as well as determining pseudo-inverse matrix. In addi-tion, the software implementation of the numerical-analytical method also contains a cus-tom implemented functions for determining the given matrix elements derivatives and for calculating the matrix discretes at the approximation center with a given scaling coeffi-cient. Algorithm flowcharts and Python source codes for all listed programs are presented. The software implementation is tested on a model example with a square matrix, for which an analytical solution is obtained using two approaches - the determination of the usual inverse one-parameter matrix and the decomposition method for determining the same matrix. This matrix is defined in exactly the same way as numerical-analytical decomposition methods.

On Properties and Structure of the Analytic Singular Value Decomposition

On Properties and Structure of the Analytic Singular Value Decomposition

Analytical Decomposition of Nodal Frequency Responses

Analytical Decomposition of Nodal Frequency Responses

Gaussian process metamodel and Markov chain Monte Carlo-based Bayesian inference framework for stochastic nonlinear model updating with uncertainties

The estimation of the posterior probability density function (PDF) of unknown parameters remains a challenge in stochastic nonlinear model updating with uncertainties; thus, a novel Bayesian inference framework based on the Gaussian process metamodel (GPM) and the advanced Markov chain Monte Carlo (MCMC) method is proposed in this paper. The instantaneous characteristics (ICs) of the decomposed measurement response, calculated using the Hilbert transform and the discrete analytical mode decomposition methodology, are extracted as nonlinear indices and further used to construct the likelihood function. Then, the posterior PDFs of structural nonlinear model parameters are derived based on the Bayesian theorem. To precisely calculate the posterior PDF, an advanced MCMC approach, i.e., delayed rejection adaptive Metropolis-Hastings (DRAM) algorithm, is adopted with the advantages of a high acceptance ratio and strong robustness. However, as a common shortage in most MCMC methods, the resampling technology is still applied, and numerous iterations of nonlinear simulations are conducted to ensure accuracy, thus directly reducing the computational efficiency of the DRAM. To address the abovementioned issue, a mathematical regression metamodel of the GPM with a polynomial kernel function is adopted in this paper instead of the traditional finite element model (FEM) to simulate a nonlinear response for the reduction of computational cost, and the hyperparameters are further estimated using the conjugate gradient optimization methodology. Finally, numerical simulations concerning a Giuffré–Menegotto–Pinto modeled steel-frame structure and a seven-storey base-isolated structure are conducted. Furthermore, a shake-table experimental test of a nonlinear steel framework is investigated to validate the accuracy of the Bayesian inference method. Both simulations and experiment demonstrate that the proposed GPM and DRAM-based Bayesian method effectively estimates the posterior PDF of unknown parameters and is appropriate for stochastic nonlinear model updating even with multisource uncertainties.

Parameter Estimation of Multiphase Machines Applicable to Variable Phase-Pole Machines

Variable phase-pole machines are envisioned in applications requiring a large torque-speed operating area. The control of these machines relies on accurate models and parameters but research on their parameter identification is scarce. This paper presents an offline parameter-identification method for variable phase-pole machines adopting a harmonic-plane decomposition model. The method employs standard tests with single-frequency three-phase excitation in multiple pole configurations and uses the results to minimize a constrained, regularized weighted least-squares problem. It relies on identifying a set of parameters common to all phase-pole configurations and transforming them into the adopted model. Good agreement is exhibited when comparing experimental results to an analytical harmonic-plane decomposition model using the inferred parameters. Steady-state, as well as pole transitions, are compared. The paper emphasizes the importance of performing measurements in multiple pole configurations and weighing these measurements appropriately to render an accurate set of parameters.

Convergence and analytic decomposition of quantum cohomology of toric bundles

We prove that the equivariant big quantum cohomology QHT⁎(E) of the total space E of a toric bundle E→B converges provided that the big quantum cohomology QH⁎(B) converges. The proof is based on Brown's mirror theorem for toric bundles [5]. It has been observed by Coates, Givental and Tseng that the quantum connection of E splits into copies of that of B[10]. Under the assumption that QH⁎(B) is convergent, we construct a decomposition of the quantum D-module of E into a direct sum of that of B, which is analytic with respect to parameters of QHT⁎(E). In particular, we obtain an analytic decomposition for the equivariant/non-equivariant big quantum cohomology of E.

Decomposition of matrix product states into shallow quantum circuits

Tensor networks (TNs) are a family of computational methods built on graph-structured factorizations of large tensors, which have long represented state-of-the-art methods for the approximate simulation of complex quantum systems on classical computers. The rapid pace of recent advancements in numerical computation, notably the rise of GPU and TPU hardware accelerators, have allowed TN algorithms to scale to even larger quantum simulation problems, and to be employed more broadly for solving machine learning tasks. The ‘quantum-inspired’ nature of TNs permits them to be mapped to parametrized quantum circuits (PQCs), a fact which has inspired recent proposals for enhancing the performance of TN algorithms using near-term quantum devices, as well as enabling joint quantum–classical training frameworks that benefit from the distinct strengths of TN and PQC models. However, the success of any such methods depends on efficient and accurate methods for approximating TN states using realistic quantum circuits, which remains an unresolved question. This work compares a range of novel and previously-developed algorithmic protocols for decomposing matrix product states (MPS) of arbitrary bond dimension into low-depth quantum circuits consisting of stacked linear layers of two-qubit unitaries. These protocols are formed from different combinations of a preexisting analytical decomposition method together with constrained optimization of circuit unitaries, with initialization by the former method helping to avoid poor-quality local minima in the latter optimization process. While all of these protocols have efficient classical runtimes, our experimental results reveal one particular protocol employing sequential growth and optimization of the quantum circuit to outperform all others, with even greater benefits in the setting of limited computational resources. Given these promising results, we expect our proposed decomposition protocol to form a useful ingredient within any joint application of TNs and PQCs, further unlocking the rich and complementary benefits of classical and quantum computation.

Abstract 15813: Machine Learning Improves Prediction of Heart Failure and Cardiovascular Death Through a Signal Analytical Approach of Echocardiography

Introduction: Recently, speckle tracking echocardiography (STE) and tissue Doppler imaging (TDI) have gained increasing traction as non-invasive tissue characterization methods within cardiology. But until now many patterns from the strain and TDI curves remain uninvestigated. Signal analytical methods like wavelet analysis have shown promising potential in effectively identifying previously unknown pathological patterns present in ECG signals. Therefore, we hypothesized that a signal analytic approach combined with supervised machine learning (ML) on strain and TDI curves could identify unknown pathophysiological deformation drivers of heart failure (HF) and cardiovascular death (CV death) in the general population. Methods: The analysis included 3781 subjects from the general population. In total 720 novel statistical parameters and wavelet signal parameters from 18 strain curves and 6 TDI curves were generated. The parameters were used to train an ensemble decision tree with 20-fold cross-validation and compared to a baseline ML model trained on 22 conventional echocardiographic parameters. Results: Follow up-time was four years. In total 108 subjects (2.9%) met the outcome. By including statistical and wavelet-derived parameters along with 22 conventional echocardiographic parameters in a combined model, the ML model was significantly improved compared to the baseline model (AUC for conventional model: 0.76 vs combined model: 0.825, p = 0.0086). Both statistical parameters, such as the mean and skewness of the TDI curve, as well as wavelet parameters, such as mean on the first decomposition level of the strain curve, were found to be important in the model. Conclusion Adding novel echocardiographic parameters based on signal analytical statistics and wavelet decomposition methods to preexisting conventional echocardiographic parameters significantly improved the prediction of incident HF or CV death in ML models.

Structural damping estimation from live monitoring of a tall modular building

AbstractThe damping ratio is a key indicator of an individual structure's susceptibility to dynamic loads, including the level of discomfort experienced by the occupants of a tall building subjected to wind loading. While computational models, laboratory studies and empirical data can provide estimates of structural damping, the most reliable way to evaluate true damping ratio values is through modal identification using data from field tests on full‐scale finished structures. As an innovative form of construction, high‐rise modular buildings have not been the subject of previous vibration monitoring investigations, implying an absence of essential structural dynamics information. This paper assesses the reliability of four modal identification methods for estimating the damping ratio of a structure using ambient acceleration response data recorded from the world's tallest modular structure, the Ten Degrees building in Croydon, South London. The methods considered are two implementations of the Bayesian fast Fourier transform (BFFT), the random decrement technique (RDT), and a hybrid of the RDT which first decomposes the ambient data into sub‐signals using analytical mode decomposition (AMD‐RDT). Each method is applied to response data collected during 10 significant wind loading events to evaluate the inherent modal properties of the structure, with the computed damping ratio values compared between methods and events. By reporting the first measured damping ratios for a tall modular structure, the paper makes an important contribution to knowledge about the vibration properties of an emerging form of construction.

Analyzing the sensitivity of wave frequency responses of floating vessels to uncertain system variables utilizing Polynomial Chaos Expansion

Abstract From a mathematical viewpoint, the frequency domain analysis of vessel motion responses due to wave actions is based on integration of system dynamics idealized in terms of response amplitude operators (RAOs) for 6 DOF rigid body motions and an input wave spectrum in order to obtain the response spectrum. Various quantities of interest can be deduced from the response spectrum which are then used for deriving response-based operational limits for marine operations, also including extreme value and fatigue analysis. The variation of such quantities, owing to the uncertainties associated with the vessel system parameters, can be quantified by performing uncertainty propagation (UP) and consequent sensitivity analysis (SA). This study emphasizes and proposes a computational-efficient way of assessing the sensitivity of the system model output with respect to the uncertainties residing in the input parameters by operating on a surrogate model representation. In this respect, the global sensitivity analysis was effectively carried out by deploying an efficient non-intrusive polynomial chaos expansion (PCE) surrogate model built using a point collocation strategy. Successively, the Sobol' indices were obtained from the analytical decomposition of the polynomial coefficients. The indices, eventually, are employed to quantitatively measure the effects of input uncertainties on the output 6 DOF vessel Root Mean Square responses.

Design and analysis of nonlinear numerical algorithm for seismic response of structures based on HVSR algorithm.

Earthquake is one of the main factors causing structural disasters in current buildings. Under earthquake action, adjacent building structures are generally in different vibration stages, and collisions may occur in the structures, which may cause serious damage to the structure. In order to prevent certain earthquakes from damaging the designed buildings, this article mainly introduced the design and analysis of a numerical algorithm for seismic nonlinear structural dynamic response based on the HVSR algorithm. This article evenly divided the acceleration response time series into 15 time periods and then selected the position corresponding to the peak point of instantaneous amplitude within each period as the selected data point position. The same seismic load can be applied at the bottom of the established nonlinear model to extract the dynamic response data of the top layer of the structure, and then, the instantaneous amplitude and corresponding instantaneous phases and frequencies of the main components of the structural dynamic response can be extracted through the time-varying filter and Hilbert transform based on the discrete analytic mode decomposition. Under the influence of these four ground motions, the collision force within the range of 0-50 kN accounted for over 87% of the total number of collisions. In the comparison results of collision response to peak displacement, the four ground motions all led to structural collision, and the collision inhibited the positive peak displacement response of node 1512. Compared with noncollision, the peak displacement was reduced by 27.273, 33.675, 27.727, and 37.248%, respectively. The peak displacement of 1512 nodes was suppressed and reduced by 18.856%. The results indicate that the HVSR algorithm can obtain the instantaneous characteristic parameters of nonlinear structural dynamic response and achieve model correction.

Optimal effect of energy resources and distributed generations on network flow using an analytical method and structural decomposition

Optimal effect of energy resources and distributed generations on network flow using an analytical method and structural decomposition

Optimal allocation of transmission fixed costs to electric vehicle charging stations and wind farms using an analytical method and structural decomposition

Renewable energies have found a suitable place in the electricity grid due to their non-pollution and cheapness. From the point of view of the grid operator, the allocation of costs should be appropriately allocated to producers and customers in competitive electricity markets. A fair allocation strategy can lead to more efficient use of current transmission lines while providing economic signals to guide future generation planning and load shedding. In this paper, first, using a powerful structural decomposition method, the optimal location of electric vehicle charging stations (EVCSs) and wind farms is determined from the flow aspect of grid lines. Then, the transmission fixed cost is assigned to each item placed in the network. The proposed method is implemented on the IEEE 24-bus network, and its results are analyzed. The fair allocation of transmission fixed costs prevents collusion, and the proposed method can be an effective tool for the network operator.