State-space Framework Research Articles

State-space analysis of a continuous gravitational wave source with a pulsar timing array: inclusion of the pulsar terms

ABSTRACT Pulsar timing arrays (PTA) can detect continuous nanohertz gravitational waves (GW) emitted by individual supermassive black hole binaries. The data analysis procedure can be formulated within a time-domain, state-space framework, in which the radio timing observations are related to a temporal sequence of latent states, namely the intrinsic pulsar spin frequency. The achromatic wandering of the pulsar spin frequency is tracked using a Kalman filter concurrently with the pulse frequency modulation induced by a GW from a single source. The modulation is the sum of terms proportional to the GW strain at the Earth and at every pulsar in the array. Here, we generalize previous state-space formulations of the PTA problem to include the pulsar terms; that is, we copy the pulsar terms from traditional, non-state-space analyses over to the state-space framework. The performance of the generalized Kalman filter is tested using astrophysically representative software injections in Gaussian measurement noise. It is shown that including the pulsar terms corrects for previously identified biases in the parameter estimates (especially the sky position of the source) which also arise in traditional matched-filter analyses that exclude the pulsar terms. Additionally, including the pulsar terms decreases the minimum detectable strain by 14 per cent. Overall, the study verifies that the pulsar terms do not raise any special extra impediments for the state-space framework, beyond those studied in traditional analyses. The inspiral-driven evolution of the wave frequency at the Earth and at the retarded time at every pulsar in the array is also investigated.

On-the-fly spectral unmixing based on Kalman filtering

This work introduces an on-the-fly (i.e., online) linear spectral unmixing method which is able to sequentially analyze spectral data acquired on a spectrum-by-spectrum basis. After deriving a sequential counterpart of the conventional linear mixing model, the proposed approach recasts the linear unmixing problem into a linear state-space estimation framework. Under Gaussian noise and state models, the estimation of the pure spectra can be efficiently conducted by resorting to Kalman filtering. Interestingly, it is shown that this Kalman filter can operate in a lower-dimensional subspace to lighten the computational burden of the overall unmixing procedure. Experimental results obtained on synthetic and real Raman data sets show that this Kalman filter-based method offers a convenient trade-off between unmixing accuracy and computational efficiency, which is crucial for operating in an on-the-fly setting. The proposed method constitutes a valuable building block for benefiting from acquisition and processing frameworks recently proposed in the microscopy literature, which are motivated by practical issues such as reducing acquisition time and avoiding potential damages being inflicted to photosensitive samples. The code associated with the numerical illustrations reported in this paper is freely available online at https://github.com/HKouakou/KF-OSU.

Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array

Abstract Continuous nanohertz gravitational waves from individual supermassive black hole binaries may be detectable with pulsar timing arrays. A novel search strategy is developed, wherein intrinsic achromatic spin wandering is tracked simultaneously with the modulation induced by a single gravitational wave source in the pulse times of arrival. A two-step inference procedure is applied within a state-space framework, such that the modulation is tracked with a Kalman filter, which then provides a likelihood for nested sampling. The procedure estimates the static parameters in the problem, such as the sky position of the source, without fitting for ensemble-averaged statistics such as the power spectral density of the timing noise, and therefore complements traditional parameter estimation methods. It also returns the Bayes factor relating a model with a single gravitational wave source to one without, complementing traditional detection methods. It is shown via astrophysically representative software injections in Gaussian measurement noise that the procedure distinguishes a gravitational wave from pure noise down to a characteristic wave strain of h0 ≈ 2 × 10−15. Full posterior distributions of model parameters are recovered and tested for accuracy. There is a bias of ≈0.3 rad in the marginalised one-dimensional posterior for the orbital inclination ι, introduced by dropping the so-called ‘pulsar terms’. Smaller biases $\lesssim 10~{{\%}}$ are also observed in other static parameters.

Risk premium, price of risk and expected volatility in the oil market: Evidence from survey data

This paper contributes to the literature on crude oil risk premiums by providing ex-ante measures of these premiums using survey oil price expectations over an extended period. These ex-ante premiums are uncorrelated with ex-post premiums commonly used in existing studies, whereas they are more relevant as they directly influence investors' decision-making. Utilizing a portfolio choice model, we explain the ex-ante premium as the product of the price of risk and the expected variance, both varying over time and across horizons. We estimate this relationship using a multivariate state-space framework. From our estimated risk prices we find, on average, that investors exhibit risk-seeking behaviour in the short term and risk aversion in the long term. It follows that the term structure of oil risk premiums are prominently upward-sloping. Additionally, consistent with the prospect theory, investors are found to be predominantly risk averse in a context of expected gains and risk-seeking in a context of expected losses. Finally, the dynamics of risk prices are shown to be driven by identifiable economic, financial, and oil market-related factors.

Exact discrete-time stability analysis of multi-DOF haptic rendering: Impact of multi-rate, time-delay, and mechanical parameters

Previous studies on the stability analysis of haptic devices have predominantly focused on single-DOF devices, thereby limiting attention to multi-DOF devices, particularly those employing multi-rate sampling schemes. In this paper, we introduce a formulation for the coupled dynamics between the haptic device and the virtual environment for a multi-DOF haptic device controlled using a dual-rate sampling scheme. Subsequently, we analyze its stability through the application of a dynamic decoupling strategy within an exact discrete-time state-space framework while the device is engaged in rendering a virtual wall along one of its operational space coordinates. Furthermore, we explore how the combined influence of the dual-rate sampling approach, time delay, and the mechanical design affects the stability boundaries of the multi-DOF haptic device at a fixed workspace location as well as within the entire usable workspace. Additionally, we utilize a model-order reduction (MOR) framework to simplify the determination of the device’s stability limits, irrespective of the specific combinations of time delay and sampling rates employed.

Mathematical Modeling on State-Space Modelling Framework and Nonlinear Analysis of Blockchain Consensus Mechanisms

Mathematical Modeling on State-Space Modelling Framework and Nonlinear Analysis of Blockchain Consensus Mechanisms

Supervised Dynamic Correlated Topic Model for Classifying Categorical Time Series

In this paper, we describe the supervised dynamic correlated topic model (sDCTM) for classifying categorical time series. This model extends the correlated topic model used for analyzing textual documents to a supervised framework that features dynamic modeling of latent topics. sDCTM treats each time series as a document and each categorical value in the time series as a word in the document. We assume that the observed time series is generated by an underlying latent stochastic process. We develop a state-space framework to model the dynamic evolution of the latent process, i.e., the hidden thematic structure of the time series. Our model provides a Bayesian supervised learning (classification) framework using a variational Kalman filter EM algorithm. The E-step and M-step, respectively, approximate the posterior distribution of the latent variables and estimate the model parameters. The fitted model is then used for the classification of new time series and for information retrieval that is useful for practitioners. We assess our method using simulated data. As an illustration to real data, we apply our method to promoter sequence identification data to classify E. coli DNA sub-sequences by uncovering hidden patterns or motifs that can serve as markers for promoter presence.

Identifying behavioral links to neural dynamics of multifiber photometry recordings in a mouse social behavior network

Objective. Distributed hypothalamic-midbrain neural circuits help orchestrate complex behavioral responses during social interactions. Given rapid advances in optical imaging, it is a fundamental question how population-averaged neural activity measured by multi-fiber photometry (MFP) for calcium fluorescence signals correlates with social behaviors is a fundamental question. This paper aims to investigate the correspondence between MFP data and social behaviors. Approach: We propose a state-space analysis framework to characterize mouse MFP data based on dynamic latent variable models, which include a continuous-state linear dynamical system and a discrete-state hidden semi-Markov model. We validate these models on extensive MFP recordings during aggressive and mating behaviors in male-male and male-female interactions, respectively. Main results: Our results show that these models are capable of capturing both temporal behavioral structure and associated neural states, and produce interpretable latent states. Our approach is also validated in computer simulations in the presence of known ground truth. Significance: Overall, these analysis approaches provide a state-space framework to examine neural dynamics underlying social behaviors and reveals mechanistic insights into the relevant networks.

Estimation of planned and unplanned missing individual scores in longitudinal designs using continuous-time state-space models.

Latent change score (LCS) models within a continuous-time state-space modeling framework provide a convenient statistical approach for analyzing developmental data. In this study, we evaluate the robustness of such an approach in the context of accelerated longitudinal designs (ALDs). ALDs are especially interesting because they imply a very high rate of planned data missingness. Additionally, most longitudinal studies present unexpected participant attrition leading to unplanned missing data. Therefore, in ALDs, both sources of data missingness are combined. Previous research has shown that ALDs for developmental research allow recovering the population generating process. However, it is unknown how participant attrition impacts the model estimates. We have three goals: (a) to evaluate the robustness of the group-level parameter estimates in scenarios with empirically plausible unplanned data missingness; (b) to evaluate the performance of Kalman scores (KS) imputations for individual data points that were expected but unobserved; and (c) to evaluate the performance of KS imputations for individual data points that were outside the age ranged observed for each case (i.e., to estimate the individual trajectories for the complete age range under study). In general, results showed lack of bias in the simulated conditions. The variability of the estimates increased with lower sample sizes and higher missingness severity. Similarly, we found very accurate estimates of individual scores for both planned and unplanned missing data points. These results are very important for applied practitioners in terms of forecasting and making individual-level decisions. R code is provided to facilitate its implementation by applied researchers. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

The effect of process variability and data quality on performance of a state-space stock assessment model

State-space modeling is an emerging approach to age structured fisheries stock assessment that can accommodate multiple sources of variability in processes like recruitment, abundance, and selectivity. By maximizing the marginal likelihood by treating yearly deviations as random effects and then integrating them from the likelihood, these models can estimate multiple process variances. Several fisheries software packages have been developed that use a state-space framework with marginal likelihood, which has increased their popularity and usage across the U.S. Atlantic coast, Canada, and Europe. However, robust testing is still needed to gauge the applicability of these models and understand how they perform under a range of realistic variability in the process or observation error. Using an assessment model fit to Gulf of Maine Haddock as a baseline, we used a simulation-estimation procedure to test if state-space stock assessment models could produce approximately unbiased and precise estimates over a range of process variances that extended from zero to well above the levels estimated in the Gulf of Maine Haddock assessment, or when observations were noisier (i.e., more variable around their true value) than had been assumed in the assessment. We fit alternative estimation models that differed in which processes errors were included (of recruitment, expected survival, and fishery selectivity). State-space models which specify random effects in all three processes produced approximately unbiased and precise estimates of biomass and exploitation for most operating models and therefore are recommended except when variability in expected survival is absent (or very low), in which case the model is unlikely to converge. A conventional statistical-catch-at-age model with recruitment estimated as a fixed effect for each year, deterministic expected survival, and constant selectivity produced estimates that were comparable to the best state-space model, but do not provide internal estimates of process variances and did not perform well when recruitment was highly variable. This work will facilitate the use of state-space stock assessment models and choosing the parameterization that will produce the most accurate output to inform future predictions and management.

Dynamic Co-Embedding Model for Temporal Attributed Networks.

In this article, we study the problem of embedding temporal attributed networks, with the goal of which is to learn dynamic low-dimensional representations over time for temporal attributed networks. Existing temporal network embedding methods only learn the representations for nodes, which are unable to capture the dynamic affinities between nodes and attributes. Moreover, existing co-embedding methods that learn the static embeddings of both nodes and attributes cannot be naturally utilized to obtain their dynamic embeddings for temporal attributed networks. To address these issues, we propose the dynamic co-embedding model for temporal attributed networks (DCTANs) based on the dynamic stochastic state-space framework. Our model captures the dynamics of a temporal attributed network by modeling the abstract belief states representing the condition of the nodes and attributes of current time step, and predicting the transitions between temporal abstract states of two successive time steps. Our model is able to learn embeddings for both nodes and attributes based on their belief states at each time step of the temporal attributed network, while the state transition tendency for predicting the future network can be tracked and the affinities between nodes and attributes can be preserved. Experimental results on real-world networks demonstrate that our model achieves substantial performance gains in several static and dynamic graph mining applications compared with the state-of-the-art static and dynamic models.

A control theoretic framework for adaptive gradient optimizers

Gradient-based optimization and control frameworks have been utilized in several applications. The learning rate parameter is typically chosen following a schedule or using methods such as line search to enhance the convergence rate. Recently, the machine learning community has developed methodologies for automated tuning of the learning rate, known as adaptive gradient methods. This paper develops a control theory-inspired framework for modeling adaptive gradient methods that solve non-convex optimization problems. We first model the adaptive gradient methods in a state–space framework, which allows us to present simpler convergence proofs of prominent adaptive optimizers, such as AdaGrad, Adam, and AdaBelief. The proposed framework is constructive because it allows synthesizing new adaptive optimizers. To illustrate this fact, we then utilize the transfer function paradigm from classical control to propose a new variant of Adam, coined AdamSSM, and prove its convergence. We add an appropriate pole-zero pair in the transfer function from squared gradients to the second moment estimate. Applications on benchmark machine learning tasks of image classification using CNN architectures and language modeling using LSTM architecture demonstrate that the AdamSSM algorithm improves the gap between generalization accuracy and faster convergence than the recent adaptive gradient methods.

An IDE-based nonlinear grey Bernoulli model and applications to daily traffic flow pattern identification

The nonlinear grey Bernoulli model is a powerful tool for modelling and forecasting time series exhibiting a rough inverted U-shape behaviour. Traditionally, it is considered an indirect dynamical model, informed by empirical knowledge that the accumulation of the inverted U-shape series leads to a growth behaviour, which is subsequently characterized by the Bernoulli ordinary differential equation (ODE). However, its mechanism remains incomplete, particularly concerning the modelling paradigm and parameter estimation. To this end, we propose an equivalent and simplified variant in the form of an integro-differential equation (IDE), enabling direct modelling of the inverted U-shaped series and thereby enhancing the interpretability. By taking the IDE as a state equation in the state space framework, separable nonlinear least squares (SLS) and nonlinear least squares (NLS) are respectively formulated to simultaneously estimate structural parameters and the initial condition. Then, by combining the state equation (ODE/IDE) and parameter estimation approach (SLS/NLS), the generated ODE-based indirect paradigms are comprehensively compared with the IDE-based direct ones. Numerical simulations show that (i) IDE-based models outperform ODE-based ones and (ii) NLS outperforms SLS. Real-world applications indicate that the nonlinear grey Bernoulli model combining IDE and NLS can accurately discover the underlying dynamics of daily traffic flow, outperforming the competitive models.

Substitution effect of tourism destinations in Türkiye: Case study of Iranian tourists

This study investigates the substitution effect between the destinations of Iranian tourists who travel to Turkey, distinguishing between Istanbul and other touristic cities. For this purpose, it uses the Dynamic Linear Regression model in the class of time-varying parameters described in a State Space framework. The data are monthly 2018-1 to 2023-2 the results show that there is a dynamic relationship between the “number of incoming Iranian tourists to Istanbul” and “the number of incoming Iranian tourists to other destinations”. It seems that the opening of Istanbul's new airport and the diversification of flights to Turkish destinations have an important factor in the dynamics of the parameter. There is a substitution effect between Istanbul and other touristic destinations. Also, inflation (both Iran and Turkey) affects Iranians' travel behavior to Turkey due to two features: One is due to the decrease in the purchasing power of Iranians and the second is due to the change in the national currency of the two countries.

Idiographic psychological networks based on intensive longitudinal data are increasingly employed in clinical practice. However, these models mainly focus on the associations among psychological variables and changes in these associations, whereas the underlying factors for those changes are not taken into account. The factors contributing to change can be studied with moderation analyses, but although such analyses are standard in

Idiographic psychological networks based on intensive longitudinal data are increasingly employed in clinical practice. However, these models mainly focus on the associations among psychological variables and changes in these associations, whereas the underlying factors for those changes are not taken into account. The factors contributing to change can be studied with moderation analyses, but although such analyses are standard in clinical research, they are hardly applied in the domain of idiographic networks. Therefore, we implement the fixed moderated time series model to study how networks change depending on context factors. Fixed moderated time series analysis is a vector autoregressive based model, in which all parameters of the model can be moderated, including the innovation structure. As the model is based on the state space framework, it can also directly estimate changes in the mean levels of the variables in the network. With two empirical examples, we demonstrate how the fixed moderated time series model can reveal changing network structures. We show that this idiographic moderation approach not only provides a new way to look at what parameters in a network change over time, but also offers tools to see which factors are associated with the change.

Impact of fishing activities on the population dynamics of European whitefish in four peri-alpine lakes

Inland fisheries play a crucial role in socio-economic activities and food production. However, these fisheries are often less intensively monitored and studied than marine fisheries. In the past two decades, important fluctuations in European whitefish (Coregonus lavaretus) landings have been observed in four peri-alpine lakes in France and Switzerland. To better gauge the impact of fishing removal, a multi-lakes Delay-Difference model was developed and adapted to these fisheries. A hierarchical state-space Bayesian framework was used to integrate stochasticity for each process and incorporate diverse data. The model gave estimates of time series for biomass, recruitment, stage-structured landings, and fishing mortality, as well as estimates of natural mortality rate, Brody growth coefficient and mean recruitment productivity. Differences in the estimates of variables predicted by the model were observed among lakes. Negative impacts of exploitation have been highlighted for Lakes Geneva, Bourget, and Annecy. Low levels of biomass under high fishing mortality rates were observed, while landings tended to increase under lower mortality rates. Lakes Geneva and Bourget outputs suggest stocks were impacted by fishing activities and that fishing effort reduction could ultimately increase yields. Lake Annecy abundance and landings trends increased after 2010, suggesting management strategies that focused on effort reduction were successful. Lake Neuchâtel stock abundance was low after 2017 and probably more fragile due to low biomass levels and recruitment. The observed changes in European whitefish biomass cannot be attributed solely to fishing, suggesting that environmental factors may also influence recruitment success alongside the impacts of fishing pressure.

A Youla Operator State-Space Framework for Stably Implementable Distributed Control

A Youla Operator State-Space Framework for Stably Implementable Distributed Control

Exploring the relationship between computational frameworks and neuroscience studies for sensorimotor learning and control

<p>The relationship between computational frameworks and neuroscience studies is crucial for understanding sensorimotor learning and control. Various tools and frameworks, such as Bayesian decision theory, neural dynamics framework, and state space framework, have been used to explore this relationship. Bayesian decision theory provides a mathematical framework for studying sensorimotor control and learning. It suggests that the central nervous system constructs estimate of sensorimotor transformations through internal models and represents uncertainty to respond optimally to environmental stimuli. The neural dynamics framework analyzes patterns of neural activity to understand the computational mechanisms underlying sensorimotor control and learning. The state space framework assesses the structure of learning in the state space and helps understand how the brain transforms sensory input into motor output. Computational frameworks have provided valuable insights into sensorimotor learning and control. They have been used to study the organization of motor memories based on contextual rules and the role of structural learning in the sensorimotor system. These frameworks have also been employed to investigate the neural dynamics under sensorimotor control and learning tasks, as well as the effect of explicit strategies on sensorimotor learning. The interplay between computational frameworks and neuroscience studies has enhanced our understanding of sensorimotor learning and control. Bayesian decision theory, neural dynamics framework, and state space framework have provided valuable tools for studying the computational mechanisms underlying these processes. They have helped uncover the role of contextual information, structural learning, and neural dynamics in sensorimotor control and learning. Further research should continue exploring the relationship between computational frameworks and neuroscience studies in sensorimotor learning and control. This interdisciplinary approach can lead to a better understanding of how motor skills are learned, retained, and improved through targeted interventions. Additionally, the application of computational frameworks in clinical settings may help develop more effective rehabilitation strategies for individuals with motor impairments.</p>

Comparison of Subspace Identification Methods for Modal Estimation of Bladed Disks

Abstract Bladed disks are critical parts of aeronautic turbojet engines requiring numerous dynamic analysis tests to fully achieve their design process. This work presents subspace state-space identification techniques for estimation of modal parameters of bladed disks using realistic although numerically generated test case data. Indeed, modal testing of bladed disks can exhibit high modal density leading to modal estimation issues. This study focuses on subspace state-space identification framework as it is an efficient way to process vector valued time series and thus to estimate modal parameters in a context of high modal density. In order to evaluate the techniques of interest, a versatile modal model has been specifically implemented to simulate data representative of full scale rotating aeronautic fan modal tests. This model is easily adjustable allowing to evaluate the identification methods in a more or less severe estimation context. The performance of the investigated methods is discussed and compared with the prescribed parameters of the model. Moreover, different techniques to estimate the order of the associated state-space model are reviewed and tested over several simulated configurations. Finally, a method to evaluate the uncertainties over the model parameters using covariance of estimator results and pseudospectrum computation is proposed and discussed over the investigated test cases.

Nonlinear grey Bernoulli model with physics-preserving Cusum operator

The Cusum (cumulative sum) operator is a fundamental prerequisite for the nonlinear grey Bernoulli model. Traditionally, it is believed to visually identify the underlying dynamic pattern of the original time series. This paper presents the misconceptions concerning the Cusum operation and the over-optimization of the initial condition in the classical nonlinear grey Bernoulli model, both of which inspire the proposal of a physics-preserving Cusum operator. Under a state space framework, separable nonlinear least squares and nonlinear least squares are formulated to generate simultaneous estimates of structural parameters and initial condition. By combining the Cusum operators and parameter estimation methods, four modeling paradigms are generated and comprehensively compared. The simulation results show that (i) the physics-preserving Cusum outperforms the traditional Cusum and (ii) nonlinear least squares outperforms separable nonlinear least squares, especially in irregular sampling settings with large time intervals and high noise levels. Finally, the proposed approach is used to identify the underlying dynamics from short-term traffic flow data, and the results validate its effectiveness.