Response Vector Research Articles

Conformal Multi‐Target Hyperrectangles

ABSTRACTWe propose conformal hyperrectangular prediction regions for multi‐target regression. We propose split conformal prediction algorithms for both point and quantile regression to form hyperrectangular prediction regions, which allow for easy marginal interpretation and do not require covariance estimation. In practice, it is preferable that a prediction region is balanced, that is, having identical marginal prediction coverage, since prediction accuracy is generally equally important across components of the response vector. The proposed algorithms possess two desirable properties, namely, tight asymptotic overall nominal coverage as well as asymptotic balance, that is, identical asymptotic marginal coverage, under mild conditions. We then compare our methods to some existing methods on both simulated and real data sets. Our simulation results and real data analysis show that our methods outperform existing methods while achieving the desired nominal coverage and good balance between dimensions.

Scaled envelope models for multivariate time series

Vector autoregressive (VAR) models have become a popular choice for modeling multivariate time series data due to their simplicity and ease of use. Efficient estimation of VAR coefficients is an important problem. The envelope technique for VAR models is demonstrated to have the potential to yield significant gains in efficiency and accuracy by incorporating linear combinations of the response vector that are essentially immaterial to the estimation of the VAR coefficients. However, inferences based on envelope VAR (EVAR) models are not invariant or equivariant upon the rescaling of the VAR responses, limiting their application to time series data that are measured in the same or similar units. In scenarios where VAR responses are measured on different scales, the efficiency improvements promised by envelopes are not always guaranteed. To address this limitation, we introduce the scaled envelope VAR (SEVAR) model, which preserves the efficiency-boosting capabilities of standard envelope techniques while remaining invariant to scale changes. The asymptotic characteristics of the proposed estimators are established based on different error assumptions. Simulation studies and real-data analysis are conducted to demonstrate the efficiency and effectiveness of the proposed model. The numerical results corroborate our theoretical findings.

Simultaneous credible bands for transfer function estimates

This paper deals with simultaneous credible bands (SCBs) for transfer function estimates based on Gaussian posteriors of the impulse response vector derived from identification of high-order FIR models, where SCBs quantify estimation errors of functions over their entire domain. Though conservative, SCBs for step responses and gain/phase functions are obtained by maximizing and minimizing them over the uncertainty sets specified by critical values of χ2 statistics associated with the Gaussian posterior. This procedure also applies to deriving (exact) pointwise credible bands (PCBs) using relevant critical values. In numerical studies, we compute the failure rates that SCBs fail to include the true step response or gain function over their respective domains; thereby an empirical method for computing less conservative SCBs is developed.

Low frequency load identification under high noise level using weighted total least squares

Load identification in structural dynamics is an ill-conditioned inverse problem, and the errors exist in both the transfer function matrix and the response vector, which have a great influence on the accuracy of the identification, especially at the low frequency and high noise. Although the Total Least Squares (TLS) method can consider the errors in the transfer function matrix and the response vector, the problem of unequal precision between them has not been properly solved. In this article, the Weighted Total Least Squares (WTLS) method for load identification is presented. First, the variance–covariance matrices are constructed using stochastic information, which can consider the unequal precision of the data and make the solution less biased and more precise. Then, Tikhonov regularization is used to regularize the WTLS method to reduce the ill-condition of the transfer function matrix. To validate the performance of the WTLS method under different noise levels, a load identification simulation with four excitation loads on a plate and a load identification experiment with three excitation loads on a steel plate were studied. The results show that when the noise levels of the transfer function and the response are different, the accuracy of the TLS solution is poor. Especially when the noise levels are high, the identification deviations are large. The WTLS method considers the unequal noise levels using the weight matrices, which provides more stable load estimates at different noise levels. And the identification deviations are greatly reduced compared to the TLS method.

Using a novel multiple-source indicator to investigate the effect of scale format on careless and insufficient effort responding in a large-scale survey experiment

Common indicator-based approaches to identifying careless and insufficient effort responding (C/IER) in survey data scan response vectors or timing data for aberrances, such as patterns signaling straight lining, multivariate outliers, or signals that respondents rushed through the administered items. Each of these approaches is susceptible to unique types of misidentifications. We developed a C/IER indicator that requires agreement on C/IER identification from multiple behavioral sources, thereby alleviating the effect of each source’s standalone C/IER misidentifications and increasing the robustness of C/IER identification. To this end, we combined a response-pattern-based multiple-hurdle approach with a recently developed screen-time-based mixture decomposition approach. In an application of the proposed multiple-source indicator to PISA 2022 field trial data we (a) showcase how the indicator hedges against (presumed) C/IER overidentification of its constituting components, (b) replicate associations with commonly reported external correlates of C/IER, namely agreement with self-reported effort and C/IER position effects, and (c) employ the indicator to study the effects of changes of scale characteristics on C/IER occurrence. To this end, we leverage a large-scale survey experiment implemented in the PISA 2022 field trial and investigate the effects of using frequency instead of agreement scales as well as approximate instead of abstract frequency scale labels. We conclude that neither scale format manipulation has the potential to curb C/IER occurrence.

Low-Complexity 2D-DOD and 2D-DOA Estimation in Bistatic MIMO Radar Systems: A Reduced-Dimension MUSIC Algorithm Approach.

This paper presents a new technique for estimating the two-dimensional direction of departure (2D-DOD) and direction of arrival (2D-DOA) in bistatic uniform planar array Multiple-Input Multiple-Output (MIMO) radar systems. The method is based on the reduced-dimension (RD) MUSIC algorithm, aiming to achieve improved precision and computational efficiency. Primarily, this pioneering approach efficiently transforms the four-dimensional (4D) estimation problem into two-dimensional (2D) searches, thus reducing the computational complexity typically associated with conventional MUSIC algorithms. Then, exploits the spatial diversity of array response vectors to construct a 4D spatial spectrum function, which is crucial in resolving the complex angular parameters of multiple simultaneous targets. Finally, the objective is to simplify the spatial spectrum to a 2D search within a 4D measurement space to achieve an optimal balance between efficiency and accuracy. Simulation results validate the effectiveness of our proposed algorithm compared to several existing approaches, demonstrating its robustness in accurately estimating 2D-DOD and 2D-DOA across various scenarios. The proposed technique shows significant computational savings and high-resolution estimations and maintains high precision, setting a new benchmark for future explorations in the field.

What does the mean mean? A simple test for neuroscience.

Trial-averaged metrics, e.g. tuning curves or population response vectors, are a ubiquitous way of characterizing neuronal activity. But how relevant are such trial-averaged responses to neuronal computation itself? Here we present a simple test to estimate whether average responses reflect aspects of neuronal activity that contribute to neuronal processing. The test probes two assumptions implicitly made whenever average metrics are treated as meaningful representations of neuronal activity: Reliability: Neuronal responses repeat consistently enough across trials that they convey a recognizable reflection of the average response to downstream regions.Behavioural relevance: If a single-trial response is more similar to the average template, it is more likely to evoke correct behavioural responses. We apply this test to two data sets: (1) Two-photon recordings in primary somatosensory cortices (S1 and S2) of mice trained to detect optogenetic stimulation in S1; and (2) Electrophysiological recordings from 71 brain areas in mice performing a contrast discrimination task. Under the highly controlled settings of Data set 1, both assumptions were largely fulfilled. In contrast, the less restrictive paradigm of Data set 2 met neither assumption. Simulations predict that the larger diversity of neuronal response preferences, rather than higher cross-trial reliability, drives the better performance of Data set 1. We conclude that when behaviour is less tightly restricted, average responses do not seem particularly relevant to neuronal computation, potentially because information is encoded more dynamically. Most importantly, we encourage researchers to apply this simple test of computational relevance whenever using trial-averaged neuronal metrics, in order to gauge how representative cross-trial averages are in a given context.

Mobile Money Use, Digital Banking Services and Velocity of Money in Ghana

Investigating the correlation between digital financial services, mobile money usage, and money velocity in Ghana, the study analysed time series data spanning from 1992 to 2022. A composite index was constructed by principal component analysis using data extracted from the world development indicators, with the components mobile money usage, digital financial services, and velocity of money. The estimation utilised an impulse response function and vector error correction model; the results indicated that mobile money, digital financial services, and money velocity are related in both the short and long term. Furthermore, the application of a standard deviation innovation to the velocity of money produced increases of both positive and negative magnitude for all the variables. This suggests that mobile money, digital banking services, and velocity of money in Ghana are interdependent in an asymmetric manner. In order to facilitate an increase in the velocity of money, the research concluded that policymakers should guarantee that a greater proportion of the population has access to mobile money and digital banking services. In addition to promoting mobile money, online banking services, and digital payment methods on purpose, the government should reduce reliance on physical currency and expedite the circulation of money. It is recommended that future longitudinal studies involving African nations employ diverse estimation techniques.

An extended modal approach for modal parameter identification of structure under the existence of harmonic excitations

The existing operational modal analysis (OMA) methods for the structure subjected to white noise and harmonic combined excitations have some limitations such as easy misjudgment of true and spurious modes and slow identification speed. Through expressing the system response with the extended modal matrix (EMM) and the extended modal response (EMR) vector, a novel operational modal parameter identification approach called the extended modal approach is proposed to obtain structural true modes under the existence of multiple harmonic excitations. The EMRs consist of the true modal responses and the spurious modal responses, and each of the former is random while each of the latter is harmonic. It is also proved theoretically that the EMM can be identified using the power spectrum density transmissibility (PSDT) method. Therefore, the extended modal approach includes three steps: (1) Using the PSDT to identify the EMM; (2) Utilizing the least squares reconstruction method to obtain the EMRs from the underdetermined extended modal equation; (3) Judging each of the EMRs to be true or spurious according to its empirical density function. Structural true modes can be ultimately obtained by removing all spurious modes from the identified results. The new approach is numerically verified through the OMA of two multiple-degree-of-freedom systems and then experimentally verified through the OMA of a test beam. The results in numerical simulation and experiments all show that the extended modal approach can identify accurately and quickly structural true modes under multiple harmonic excitations. Besides, the approach has good robustness against noise contamination.

Non-uniformity correction algorithm for DoFP adapted to integration time variations.

Division of the focal plane (DoFP) polarization detector is a pivotal technology in real-time polarization detection. This technology integrates a micropolarization array (MPA) onto the conventional focal plane, introducing a more intricate non-uniformity than traditional focal plane detectors. Current non-uniformity correction algorithms for DoFP are difficult to adapt to changes in integration time and perform poorly in low-polarization scenarios. Analyzing the characteristics of DoFP, formulating a pixel response model, and introducing an adaptive non-uniformity correction algorithm tailored for varying integration time. The DoFP analysis vectors are decomposed into average polarization response and unit analysis vectors for correction separately to improve the performance of the correction algorithm in different polarization scenarios. The performance of modern correction algorithms was tested and evaluated using standard uniform images, and the proposed method outperformed existing algorithms in terms of polarization measurement accuracy under the root mean square error (RMSE) metric. Moreover, in natural scene images, our proposed algorithm shows favorable visual effects and distinguishes itself from its superior stability amid changes in the integration time.

A Nonredundant SVD-based Precoding Matrix for Blind Channel Estimation in CP-OFDM Systems Over Channels with Memory

In this paper, we investigate blind channel estimation in cyclic, prefixed orthogonal frequency division multiplexing (OFDM) systems using precoding matrices. Many studies show how the performance of bit error rate (BER) and mean square error of channel estimation are impacted by using a circulant matrix as a precoding matrix. We investigate a new structure for the precoding matrix in which the first row is generated by an exponentially decreasing equation along with the Toeplitz function and deploying singular value decomposition (SVD) to generate the final precoder matrix. This type of SVD-based precoding matrix has been presented and simulated under various circumstances. The resulting precoding matrix is employed in two different OFDM systems to estimate the channel frequency response vector up to scalar ambiguity. The proof of the precoding matrix full rank property is presented, along with other criteria that help with the development of various precoding matrices.

Robust variable selection under cellwise contamination

Cellwise outliers are widespread in real world data analysis. Traditional robust methods may fail when applied to datasets under such contamination. We introduce a variable selection procedure, that uses the Gaussian rank estimator to obtain an initial empirical covariance matrix among the response and potential predictors. We re-parameterize the classical linear regression model design matrix and the response vector such that we are able to take advantage of these robustly estimated components before applying the adaptive Lasso to obtain consistent variable selection results. The procedure is robust to cellwise outliers in low and high-dimensional settings. Empirical results show good performance compared with recently proposed robust techniques, particularly in the challenging environment when contamination rates are high but the magnitude of outliers is moderate.

Validating an algebraic approach to characterizing resonator networks

Resonator networks are ubiquitous in natural and engineered systems, such as solid-state materials, electrical circuits, quantum processors, and even neural tissue. To understand and manipulate these networks it is essential to characterize their building blocks, which include the mechanical analogs of mass, elasticity, damping, and coupling of each resonator element. While these mechanical parameters are typically obtained from response spectra using least-squares fitting, this approach requires a priori knowledge of all parameters and is susceptible to large error due to convergence to local minima. Here we validate an alternative algebraic means to characterize resonator networks with no or minimal a priori knowledge. Our approach recasts the equations of motion of the network into a linear homogeneous algebraic equation and solves the equation with a set of discrete measured network response vectors. For validation, we employ our approach on noisy simulated data from a single resonator and a coupled resonator pair, and we characterize the accuracy of the recovered parameters using high-dimension factorial simulations. Generally, we find that the error is inversely proportional to the signal-to-noise ratio, that measurements at two frequencies are sufficient to recover all parameters, and that sampling near the resonant peaks is optimal. Our simple, powerful tool will enable future efforts to ascertain network properties and control resonator networks in diverse physical domains.

An extrapolation approach within the Wiener path integral technique for efficient stochastic response determination of nonlinear systems

An extrapolation approach within the Wiener path integral (WPI) technique is developed for determining the stochastic response of diverse nonlinear dynamical systems. Specifically, the WPI technique treats the system response joint transition probability density function (PDF) as a functional integral over the space of all possible paths connecting the initial and the final states of the response vector. Further, the functional integral is evaluated, ordinarily, by considering the contribution only of the most probable path. This corresponds to an extremum of the functional integrand, and is determined by solving a functional minimization problem that takes the form of a deterministic boundary value problem (BVP). This BVP corresponds to a specific grid point of the response PDF domain. Remarkably, the BVPs corresponding to two neighboring grid points not only share the same equations, but also the boundary conditions differ only slightly. This unique aspect of the technique is exploited herein. Specifically, it is shown that solution of a BVP and determination of the response PDF value at a specific grid point can be used for extrapolating and estimating efficiently the PDF values at neighboring points without the need for considering additional BVPs. Notably, the herein developed approach enhances significantly the computational efficiency of the WPI technique without, practically, affecting the associated degree of accuracy. Two numerical examples relating to a Duffing nonlinear oscillator subjected to combined stochastic and deterministic periodic loading, and to an oscillator with asymmetric nonlinearities and fractional derivative elements are considered to demonstrate the reliability of the extrapolation approach. Juxtapositions with pertinent Monte Carlo simulation data are included as well.

Multi-response Regression for Block-missing Multi-modal Data without Imputation.

Multi-modal data are prevalent in many scientific fields. In this study, we consider the parameter estimation and variable selection for a multi-response regression using block-missing multi-modal data. Our method allows the dimensions of both the responses and the predictors to be large, and the responses to be incomplete and correlated, a common practical problem in high-dimensional settings. Our proposed method uses two steps to make a prediction from a multi-response linear regression model with block-missing multi-modal predictors. In the first step, without imputing missing data, we use all available data to estimate the covariance matrix of the predictors and the cross-covariance matrix between the predictors and the responses. In the second step, we use these matrices and a penalized method to simultaneously estimate the precision matrix of the response vector, given the predictors, and the sparse regression parameter matrix. Lastly, we demonstrate the effectiveness of the proposed method using theoretical studies, simulated examples, and an analysis of a multi-modal imaging data set from the Alzheimer's Disease Neuroimaging Initiative.

Tire Performance and Testing under Longitudinal and Combined Slip States: Induced vs Resultant Wheel-Related Slip

ABSTRACT Tires influence many overall vehicle characteristics, including safety, performance, comfort, and handling. Testing is needed to characterize tires for the selection of original equipment manufacturers submissions as well as for the development of other suspension and chassis components. The reality that tire responses are highly nonlinear and change significantly with temperature, wear, and surface pairing makes testing to adequately characterize tires for vehicle development difficult. Furthermore, achieving robust, repeatable braking and driving measurements is particularly challenging. Unlike cornering tests, the test rig input is directly opposed to the tire response vector. Moreover, using an estimated parameter (e.g., slip ratio) as a control value prohibits a clear distinction between the linear test rig input and the nonlinear tire response. In this paper, the influence of the wheel-related slip control on tire performance under longitudinal and combined slip conditions is investigated. Two different tire types are measured in a laboratory environment on an MTS Flat-Trac CT+ tire test rig. A variety of test procedures are used to consider the influence of slip and torque rates under different operating conditions (e.g., wheel loads). A recommendation is given for a low-wear and cost-efficient testing methodology for an improved assessment of tire longitudinal and combined slip characteristics by using a linear test rig input.

On the existence, uniqueness and calculation of Wiener path integral most probable paths for determining the stochastic response of nonlinear dynamical systems

Various techniques are developed for addressing the existence, uniqueness and numerical calculation of Wiener path integral (WPI) most probable path solutions. Specifically, the WPI technique for determining the stochastic response of diverse nonlinear dynamical systems treats the system response joint transition probability density function as a functional integral over the space of all possible paths connecting the initial and the final states of the response vector. This functional integral is evaluated, ordinarily, by resorting to an approximate approach that considers the contribution only of the most probable path. The most probable path corresponds to an extremum of the functional integrand and is determined by solving a functional minimization problem that takes the form of a deterministic boundary value problem (BVP).In this paper, first, it is shown that for the commonly considered case of the system nonlinearity being of polynomial form, there exist globally optimal solutions corresponding to the most probable path BVP. Further, relying on algebraic geometry concepts and tools, a condition is derived for determining if the BVP for the most probable path exhibits a unique solution over a specific region. Furthermore, a novel solution approach is developed for the BVP by relying on Sylvester’s dialytic method of elimination. Notably, the method reduces the complexity of the BVP system of coupled multivariate polynomial equations by eliminating one or more variables. Various numerical examples pertaining to diverse nonlinear oscillators are included for demonstrating the capabilities of the developed techniques.

A protocol for evaluating the entomological impact of larval source reduction on mosquito vectors at hotel compounds in Zanzibar.

There is an increasing awareness of the association between tourism activity and risks of emerging mosquito-borne diseases (MBDs) worldwide. In previous studies we showed that hotels in Zanzibar may play an important role in maintaining residual foci of mosquito vectors populations of public health concern. These findings indicated larval sources removal (LSR) interventions may have a significant negative impact on vector communities. However, a thorough analysis of the response vector species to potential LSM strategies must be evaluated prior to implementation of a large-scale area-wide control campaign. Here we propose a protocol for evaluation of the impact of LSR against mosquito vectors at hotel settings in Zanzibar. This protocol is set to determine the efficacy of LSR in a randomized control partial cross-over experimental design with four hotel compounds representing the unit of randomization for allocation of interventions. However, the protocol can be applied to evaluate the impact of LRS in more than four sites. Proposed interventions are active removal of disposed containers, and installation of water dispenser to replace single use discarded plastic water bottles, which were identified as the most important source of mosquitoes studied hotels. The ideal time for allocating intervention to the intervention arms the dry season, when the mosquito abundance is predictably lower. The possible impact of interventions on mosquito occurrence and abundance risks is then evaluated throughout subsequent rainy and dry seasons. If an appreciable reduction in mosquito abundance and occurrence risks is observed during the trial period, intervention could be extended to the control arm to determine whether any potential reduction of mosquito density is reproducible. A rigorous evaluation of the proposed LRS interventions will inspire large scale trials and provide support for evidence-based mosquito management at hotel facilities in Zanzibar and similar settings.

Channel Estimation for LEO Satellite Massive MIMO OFDM Communications

In this paper, we investigate the massive multiple-input multiple-output orthogonal frequency division multiplexing channel estimation for low-earth-orbit satellite communication systems. First, we use the angle-delay domain channel to characterize the space-frequency domain channel. Then, we show that the asymptotic minimum mean square error (MMSE) of the channel estimation can be minimized if the array response vectors of the user terminals (UTs) that use the same pilot are orthogonal. Inspired by this, we design an efficient graph-based pilot allocation strategy to enhance the channel estimation performance. In addition, we devise a novel two-stage channel estimation (TSCE) approach, in which the received signals at the satellite are manipulated with per-subcarrier space domain processing followed by per-user frequency domain processing. Moreover, the space domain processing of each UT is shown to be identical for all the subcarriers, and an asymptotically optimal vector for the per-subcarrier space domain linear processing is derived. The frequency domain processing can be efficiently implemented by means of the fast Toeplitz system solver. Simulation results show that the proposed TSCE approach can achieve a near performance to the MMSE estimation with much lower complexity.

Advanced structural health monitoring and damage detection using inverse methods and perturbation stiff-ness matrix analysis

Sensor technology advancements have the health monitoring task for modern intricate structures introduce many challenges, primarily centered around the augmentation of safety margins and operational dependabil-ity. The demand for diverse systems or methodologies is, therefore, increasing. These systems or methodolo-gies should be capable of detecting damage, monitoring remotely, and conducting continuous evaluations in real-time. As part of this study, inverse techniques rooted in wave propagation analysis within structural frameworks are utilized to identify damage response vectors. Additionally, mathematical formulations grounded in minimal rank perturbation theory facilitate determining a perturbed stiffness matrix for a com-promised structure. Various excitations are included in the analysis, which is based on intricate non-linear structural modeling. Using streamlined procedures, these findings confirm the inherent versatility of a range of methodologies capable of meeting both rapid monitoring needs and exhaustive analytical needs. In addition, the proposed approach promotes the use of intelligent structures embedded with a variety of sensors that are not restricted by limitations related to sensor type or spatial deployment. Monitoring structural health and detecting damage could be significantly improved by this strategic deployment.