Time-varying Coefficients Research Articles

Bayesian inference of structured latent spaces from neural population activity with the orthogonal stochastic linear mixing model.

The brain produces diverse functions, from perceiving sounds to producing arm reaches, through the collective activity of populations of many neurons. Determining if and how the features of these exogenous variables (e.g., sound frequency, reach angle) are reflected in population neural activity is important for understanding how the brain operates. Often, high-dimensional neural population activity is confined to low-dimensional latent spaces. However, many current methods fail to extract latent spaces that are clearly structured by exogenous variables. This has contributed to a debate about whether or not brains should be thought of as dynamical systems or representational systems. Here, we developed a new latent process Bayesian regression framework, the orthogonal stochastic linear mixing model (OSLMM) which introduces an orthogonality constraint amongst time-varying mixture coefficients, and provide Markov chain Monte Carlo inference procedures. We demonstrate superior performance of OSLMM on latent trajectory recovery in synthetic experiments and show superior computational efficiency and prediction performance on several real-world benchmark data sets. We primarily focus on demonstrating the utility of OSLMM in two neural data sets: μECoG recordings from rat auditory cortex during presentation of pure tones and multi-single unit recordings form monkey motor cortex during complex arm reaching. We show that OSLMM achieves superior or comparable predictive accuracy of neural data and decoding of external variables (e.g., reach velocity). Most importantly, in both experimental contexts, we demonstrate that OSLMM latent trajectories directly reflect features of the sounds and reaches, demonstrating that neural dynamics are structured by neural representations. Together, these results demonstrate that OSLMM will be useful for the analysis of diverse, large-scale biological time-series datasets.

Enhancing long-term survival prediction with two short-term events: Landmarking with a flexible varying coefficient model.

Patients with cardiovascular diseases who experience disease-related short-term events, such as hospitalizations, often exhibit diverse long-term survival outcomes compared to others. In this study, we aim to improve the prediction of long-term survival probability by incorporating two short-term events using a flexible varying coefficient landmark model. Our objective is to predict the long-term survival among patients who survived up to a pre-specified landmark time since the initial admission. Inverse probability weighting estimation equations are formed based on the information of the short-term outcomes before the landmark time. The kernel smoothing method with the use of cross-validation for bandwidth selection is employed to estimate the time-varying coefficients. The predictive performance of the proposed model is evaluated and compared using predictive measures: area under the receiver operating characteristic curve and Brier score. Simulation studies confirm that parameters under the landmark models can be estimated accurately and the predictive performance of the proposed method consistently outperforms existing methods that either do not incorporate or only partially incorporate information from two short-term events. We demonstrate the practical application of our model using a community-based cohort from the Atherosclerosis Risk in Communities (ARIC) study.

Unified preassigned performance-guaranteed tracking control for systems with unknown control direction

This paper suggests a unified tracking control scheme for systems suffering from unknown control direction and preassigned performance requirement. Distinguished from the existing Nussbaum function-based control methods, the presented approach achieves a unified control framework that encompasses the asymptotic or finite-time stability by introducing sliding mode technique when the nonlinear systems suffer from the unknown control direction issue. Two kinds of stabilities can be obtained only via choosing specific functions. Moreover, the suggested control approach can also deal with the changing of control direction. The stability is analyzed, and the total method rigorously guarantees the tracking errors’ required performance criterion. The simulation results of the second order inverted pendulum model serve as verification of the proposed method. Furthermore, as an alternative application scenario, the attitude tracking issue of hypersonic vehicles is dealt with by the presented method subjected with the time-varying control coefficient.

Online monitoring of profiles via RVC model with an application to industrial busbar

ABSTRACT Profile monitoring is used to check the stability of the functional relationship of the process response on several predictors. In most of the existing literature, the monitored functional relationship usually involves only one covariate and the coefficient of the covariate is assumed to be constant. In some applications, the process response depends on multiple covariates, and the functional relationship is not constant but dynamic over time, which is different from those studied in the literature. To implement profile monitoring in these applications, a semiparametric random time-varying coefficient model is employed to characterize this dynamic relationship over time. Based on this model, a profile monitoring scheme integrated with dynamic probability control limits is proposed, which can adapt to the case of the within-profile autocorrelation and arbitrary design points. In Phase I, this paper uses a backfitting iterative procedure with the REML-Based EM-Algorithm to estimate the model. In Phase II, an exponentially weighted moving average scheme on residuals with dynamic probability control limits is developed. The simulation results show that the proposed scheme performs better in many scenarios. Finally, an application to industrial busbar running process monitoring is given to illustrate the scheme’s implementation.

Towards humanlike grasp in robotic hands: mechanical implementation of force synergies

In the field of robotic hands, finger force coordination is usually achieved by complex mechanical structures and control systems. This study presents the design of a novel transmission system inspired from the physiological concept of force synergies, aiming to simplify the control of multifingered robotic hands. To this end, we collected human finger force data during six isometric grasping tasks, and force synergies (i.e. the synergy weightings and the corresponding activation coefficients) were extracted from the concatenated force data to explore their potential for force modulation. We then implemented two force synergies with a cable-driven transmission mechanism consisting of two spring-loaded sliders and five V-shaped bars. Specifically, we used fixed synergy weightings to determine the stiffness of the compression springs, and the displacements of sliders were determined by time-varying activation coefficients. The derived transmission system was then used to drive a five-finger robotic hand named SYN hand. We also designed a motion encoder to selectively activate desired fingers, making it possible for two motors to empower a variety of hand postures. Experiments on the prototype demonstrate successful grasp of a wide range of objects in everyday life, and the finger force distribution of SYN hand can approximate that of human hand during six typical tasks. To our best knowledge, this study shows the first attempt to mechanically implement force synergies for finger force modulation in a robotic hand. In comparison to state-of-the-art robotic hands with similar functionality, the proposed hand can distribute humanlike force ratios on the fingers by simple position control, rather than resorting to additional force sensors or complex control strategies. The outcome of this study may provide alternatives for the design of novel anthropomorphic robotic hands, and thus show application prospects in the field of hand prostheses and exoskeletons.

Fully distributed event-triggered formation-containment control for heterogeneous multi-agent systems with guaranteed positive MTI

In this work, we address the event-triggered output formation-containment control problem for heterogeneous multi-agent systems with multiple leaders. The aim is to achieve formation of follower agents and containment of multiple leaders by designing fully distributed event-triggered control strategy, while the minimum triggering interval (MTI) is guaranteed to be strictly positive, which is a stronger condition than simply excluding Zeno behavior. First, an output feedback fully distributed control law is proposed. Then, a novel event-triggering mechanism (ETM) is designed by introducing an auxiliary function with time-varying coefficients. By means of the auxiliary function, the time it takes for the auxiliary function to decrease from given initial condition to zero can be imposed to be the MTI. Moreover, a novel Lyapunov function depending on the auxiliary function and error term is constructed for stability analysis and control design. Finally, the effectiveness of the obtained results is illustrated by simulation results.

Forecasting carbon prices under diversified attention: A dynamic model averaging approach with common factors

To improve the predictability of carbon prices under diversified attention, this paper develops a dynamic model averaging approach with common factors (DMA-CF) which uses dimension-reduction techniques to extract factors from all models including the subsets of attention predictors and allows time-varying coefficients and model switching. The in-sample results using univariate models reveal the strong predictive power of the attention measured by the Google search volume index (AGSVI). The out-of-sample results confirm it as the strongest attention predictor, and show the superior performance of DMA-CFs relative to the original DMA and the benchmark. We further investigate how common factors improve the forecasting performance of DMA. The empirical evidence indicates that common factors efficiently aggregate the information and reduce the estimation errors in complicated models which are assigned with higher probability in DMA-CFs than in DMA, thereby digging out more predictive information for forecasting carbon prices. Moreover, DMA primarily depends on AGSVI, with the highest weights, while DMA-CFs slightly downweight the AGSVI and allocate more weight to the attention proxy of abnormal trading volume (AAVol) which provides complementary information. Finally, our DMA-CF methods can improve the economic gains in the portfolio exercise with carbon futures.

Modeling Implied Volatility Surface Using B-Splines with Time-Dependent Coefficients Predicted by Tree-Based Machine Learning Methods

Implied volatility is known to have a string structure (smile curve) for a given time to maturity and can be captured by the B-spline. The parameters characterizing the curves can change over time, which complicates the modeling of the implied volatility surface. Although machine learning models could improve the in-sample fitting, they ignore the structure in common over time and might have poor prediction power. In response to these challenges, we propose a two-step procedure to model the dynamic implied volatility surface (IVS). In the first step, we construct the bivariate tensor-product B-spline (BTPB) basis to approximate cross-sectional structures, under which the surface can be represented by a vector of coefficients. In the second step, we allow for the time-dependent coefficients and model the dynamic coefficients with the tree-based method to provide more flexibility. We show that our approach has better performance than the traditional linear models (parametric models) and the tree-based machine learning methods (nonparametric models). The simulation study confirms that the tensor-product B-spline is able to capture the classical parametric model for IVS given different sample sizes and signal-to-noise ratios. The empirical study shows that our two-step approach outperforms the traditional parametric benchmark, nonparametric benchmark, and parametric benchmark with time-varying coefficients in predicting IVS for the S&P 500 index options in the US market.

Fiscal sustainability, fiscal reactions, pitfalls and determinants

ABSTRACT We examine the sustainability of public finances and its determinants for 19 Eurozone countries from 1995 to 2020. We conclude for the existence of panel cointegration between government revenues and expenditures; primary government balance and lagged public debt-to-GDP ratio; and public debt-to-GDP ratio and lagged primary government balance. The estimated fiscal reaction functions suggest the existence of a Ricardian fiscal regime, although there is also evidence of a non-Ricardian fiscal behaviour. Finally, modelling via time-varying coefficients, we find that fiscal sustainability increases with the output gap, fiscal rules indices and current account balances. Inflation and sovereign ratings assigned by the main rating agencies produce mixed results.

A Fuzzy Neural Network-Based Intelligent Warning Method for Financial Risk of Enterprises

The fast warning for financial risk of enterprises has always been a realistic demand for their managers. Currently, this mainly relies on expert experience to make comprehensive analysis from massive business data. Benefitting from the strong computational performance of deep learning, this paper proposes a fuzzy neural network (FNN)-based intelligent warning method for financial risk of enterprises. An improved FNN structure with time-varying coefficients and time-varying time lags is established to extract features of enterprises from complex financial context. The algorithm of fuzzy C-means and fuzzy clustering based on sample data are studied. In this paper, the fuzzy C-means algorithm is used to cluster the samples, the input sample set is preprocessed, a new set of learning samples is formed, and then the neural network is trained. The enterprise financial risk sample and its modular FNN model are established, and the evaluation of the enterprise financial risk sample is simulated. Then, a decision part is added following the FNN part to output the warning results. After that, we have also conducted a case study as simulation experiments to evaluate the proposed technical framework. The obtained results show that it can perform well in the fast warning of financial risk for enterprises.

Novel Insights into Estimation of Bilinear Time Series Models with Exponential and Symmetric Coefficients

This paper focuses on the estimation and simulation of a specific subset of bilinear time series models characterized by dynamic exponential coefficients. Employing an exponential framework, we delve into the implications of the exponential function for our estimation process. Our primary aim is to estimate the coefficients of the proposed model using exponential coefficients derived from time-varying parameters. Through this investigation, our goal is to shed light on the asymptotic behaviors of the estimators and scrutinize their existence and probabilistic traits, drawing upon the foundational theorem established by Klimko and Nilsen. The least squares approach is pivotal in both estimating coefficients and analyzing estimator behavior. Moreover, we present a practical application to underscore the real-world implications of our research. By offering concrete examples of applications and simulations, we endeavor to provide readers with a comprehensive understanding of the implications of our work within the realm of time series analysis, specifically focusing on bilinear models and time-varying exponential coefficients. This multifaceted approach underscores the potential impact and practical relevance of our findings, contributing to the advancement of the field of time series analysis. To discern the symmetry characteristics of the model, we estimate it using coefficients that sum to zero and conduct a brief comparative analysis of two bilinear models.

Multi-segment droop control and optimal parameter setting strategy of wind turbine for frequency regulation

Traditionally, virtual inertia is used as the control strategy for wind turbines when participating in frequency regulation. However, it has inherent defects in measurement error amplification due to the frequency differential. Also, when control delay of wind turbines is taken into consideration, virtual inertia is essentially a fast power response, just the same as droop control. Hence, considering the adaptability of droop control, it is valuable to explore a novel droop control method without virtual inertia, as the frequency response model of wind turbines. For this reason, a multi-segment droop control strategy is proposed to provide a reliable frequency regulation model for wind turbines that can be broadly applied to other inverter-based power sources. Firstly, based on the extended system frequency response model, a differential equation including piecewise time-varying coefficients is established, and the analytical expression of the frequency response is obtained using the impulse function balancing principle and the integration by parts algorithm. Subsequently, based on analytical expression, the performance of the presented strategy is theoretically analyzed via comparison with virtual inertia control, and the conclusion that the presented multi-segment droop control has better frequency regulation performance can be got. Furthermore, to achieve optimal frequency regulation performance, a Lagrangian function is established to determine the optimal parameters of the proposed control strategy. Finally, the performance of the proposed strategy was verified in a two-area system model constructed on MATLAB/Simulink. Results show that the proposed multi-segment droop control has better frequency regulation performance.

Effect of time-varying friction coefficient on self-excited vibration of floating spline-rotor system

Different lubrication states seriously affect the stability and safety of the aviation power transmission system. This study investigates how time-varying friction coefficients impact the stability of an aviation spline-rotor system using a spline-rotor model that considers uneven stress distribution on the tooth surface. Experimental tests with a high-frequency friction and wear test machine yield time-varying friction coefficients for splines with different lubrication, surface roughness, and materials. A sharp change of friction coefficient for the sample occurs under wear debris lubrication. The average friction coefficient for the sample with roughness 1.6 is lower than those with roughness 0.8 and 3.2. Under the same lubrication conditions, the friction coefficient of Resin matrix composites is smaller than that of metallic materials. Dynamic simulation of the spline-rotor model considering time-varying friction coefficients shows rich self-excited vibration behaviors influenced by lubrication, surface roughness, and materials.

The Predictive Power of Monetary Policy on International Stock Market Returns—Evidence From TV-ARMAX Model

In this paper, we apply the time-varying ARMA model with exogenous variable (TV-ARMAX) to examine the predictive power of monetary policy on international stock returns. This method allows time-varying coefficient estimates and uses time-dependent cumulated variation penalty to filter noisy outlier data points. Based on a wide range of 31 countries, our method robustly outperforms other popular methods including the simple linear-regression model (SLM), the vector autoregression and its variants (VAR, TV-VAR, and VARX) and the ARMA model with exogenous variable (ARMAX).

Exponential Decay for a Time-Varying Coefficients Wave Equation with Dynamic Boundary Conditions

Exponential Decay for a Time-Varying Coefficients Wave Equation with Dynamic Boundary Conditions

Assessing the impact of resource efficiency, renewable energy R&D spending, and green technologies on environmental sustainability in Germany: Evidence from a Wavelet Quantile-on-Quantile Regression

One important challenge in the world today is how to reverse the growth of carbon dioxide emissions to save the planet from environmental degradation without putting economic growth at risk. Several measures and initiatives such as resource efficiency, green energy transition, energy technologies, emission control, etc. Have been adopted by several countries worldwide in order to mitigate CO2 emissions. This study investigates the impact of resource efficiency, renewable energy Research and Development (R&D) expenditures, and green technologies towards fostering environmental sustainability in Germany. Using quarterly data spanning from 1974 to 2019, the study applies the Wavelet Quantile-on-Quantile Regression (WQQR) approach. This method embeds a wavelet kernel into quantile-on-quantile regression to capture the time-varying coefficients. The empirical findings reveal a negative impact of resource efficiency, renewable energy R&D expenditures, and green technologies on energy-based carbon intensity. The results further reveal that, with the exception of green technologies, the negative effects of resource efficiency and renewable energy R&D expenditures are stronger in the middle quantiles. The study demonstrates the robustness of these results through the wavelet quantile regression analysis. Finally, the study offers valuable policy implications that align with the United Nations’ Sustainable Development Goals (SDGs) 7 and 13, aiming to achieve a sustainable environment.

A Symmetric Kernel Smoothing Estimation of the Time-Varying Coefficient for Medical Costs

In longitudinal studies, subjects are repeatedly observed at a set of distinct time points until the terminal event time. The time-varying coefficient model extends the parametric method and captures the dynamic trajectories of time-dependent covariate effects, thus enabling it to describe the potential relationship between the longitudinal variable and the observed time points. In this study, we propose a novel approach to the estimation of medical costs using a symmetric kernel smoothing method in the time-varying coefficient joint model. A smooth function of medical costs is derived by weighting the values of longitudinal data at all distinct observed time points via the combination of the kernel method and the inverse probability weighting method. For the simulation study, we first set up the true functions of time-varying coefficients; we then generated random samples for covariates and censored survival times. Subsequently, the longitudinal data of response variables could be produced. Further, numerical simulation experiments were conducted by using the proposed method and applying R code to the generated data. The estimated results for the parameters and non-parametric functions were compared with different settings. The numerical results illustrate that as the sample size increases, the bias and model-based standard errors decrease, and the performance improves with larger sample sizes. The estimates of functions in the model almost coincide with the true functions, as shown in the figures of the simulation study. Furthermore, the consistency of the obtained estimator is demonstrated via theoretical analysis, and a numerical simulation is performed to illustrate the performance of the proposed estimators. The proposed model is applied to a real-world data set acquired from a multicenter automatic defibrillator implantation trial (MADIT).

Empirical stream thermal sensitivity cluster on the landscape according to geology and climate

Abstract. Climate change is modifying river temperature regimes across the world. To apply management interventions in an effective and efficient fashion, it is critical to both understand the underlying processes causing stream warming and identify the streams most and least sensitive to environmental change. Empirical stream thermal sensitivity, defined as the change in water temperature with a single degree change in air temperature, is a useful tool to characterize historical stream temperature conditions and to predict how streams might respond to future climate warming. We measured air and stream temperature across the Snoqualmie and Wenatchee basins, Washington, during the hydrologic years 2015–2021. We used ordinary least squares regression to calculate seasonal summary metrics of thermal sensitivity and time-varying coefficient models to derive continuous estimates of thermal sensitivity for each site. We then applied classification approaches to determine unique thermal sensitivity regimes and, further, to establish a link between environmental covariates and thermal sensitivity regimes. We found a diversity of thermal sensitivity responses across our basins that differed in both timing and magnitude of sensitivity. We also found that covariates describing underlying geology and snowmelt were the most important in differentiating clusters. Our findings and our approach can be used to inform strategies for river basin restoration and conservation in the context of climate change, such as identifying climate-insensitive areas of the basin that should be preserved and protected.

Application of the adaptive method to determine the process noise in the extended Kalman filter to estimate the parameters of the two dimensional inverse heat transfer problem

To deal with inverse nonlinear heat transfer problems in a two-dimensional heat conduction problem, this paper presents a hybrid approach combining fuzzy logic and the extended Kalman filter (EKF). The proposed algorithm has been applied to the real-time reconstruction of the temperature field, time-varying convective heat transfer coefficient, and time-varying boundary heat flux using temperature data from a set of sensors. The effects of the covariance of the initial estimation error, the time step of data acquisition by the sensors, and the number of installed sensors on the precision and stability of the estimation results has been investigated by numerical experiments. To compare and validate the results, all these parameters were investigated using the EKF method. The results show that the adaptive fuzzy extended Kalman filter (FEKF) method for estimating temperature, convection coefficient, and heat flux at the boundaries is precise and stable. The comparison shows that the performance of the FEKF method in parameter estimation is better than the EKF method, and the highest increase in precision and stability of the results is related to the convective heat transfer coefficient.

From the classical Frenet–Serret apparatus to the curvature and torsion of quantum-mechanical evolutions. Part II. Nonstationary Hamiltonians

In this paper, we present a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by state vectors evolving under nonstationary Hamiltonians. Specifically, relying on the existing geometric viewpoint for stationary Hamiltonians, we discuss the generalization of our theoretical construct to time-dependent quantum-mechanical scenarios where both time-varying curvature and torsion coefficients play a key role. Specifically, we present a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced out by a parallel-transported pure quantum state evolving unitarily under a time-dependent Hamiltonian specifying the Schrödinger evolution equation. The time-varying curvature coefficient is specified by the magnitude squared of the covariant derivative of the tangent vector [Formula: see text] to the state vector [Formula: see text] and measures the bending of the quantum curve. The time-varying torsion coefficient, instead, is given by the magnitude squared of the projection of the covariant derivative of the tangent vector [Formula: see text] to the state vector [Formula: see text], orthogonal to [Formula: see text] and [Formula: see text] and, in addition, measures the twisting of the quantum curve. We find that the time-varying setting exhibits a richer structure from a statistical standpoint. For instance, unlike the time-independent configuration, we find that the notion of generalized variance enters nontrivially in the definition of the torsion of a curve traced out by a quantum state evolving under a nonstationary Hamiltonian. To physically illustrate the significance of our construct, we apply it to an exactly soluble time-dependent two-state Rabi problem specified by a sinusoidal oscillating time-dependent potential. In this context, we show that the analytical expressions for the curvature and torsion coefficients are completely described by only two real three-dimensional vectors, the Bloch vector that specifies the quantum system and the externally applied time-varying magnetic field. Although we show that the torsion is identically zero for an arbitrary time-dependent single-qubit Hamiltonian evolution, we study the temporal behavior of the curvature coefficient in different dynamical scenarios, including off-resonance and on-resonance regimes and, in addition, strong and weak driving configurations. While our formalism applies to pure quantum states in arbitrary dimensions, the analytic derivation of associated curvatures and orbit simulations can become quite involved as the dimension increases. Thus, finally we briefly comment on the possibility of applying our geometric formalism to higher-dimensional qudit systems that evolve unitarily under a general nonstationary Hamiltonian.