Valid model-free spatial prediction.

Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in non-stationary cases, model-based prediction intervals are at risk of misspecification bias that can negatively affect their validity. Here we present a new approach for model-free nonparametric spatial prediction based on the conformal prediction machinery. Our key observation is that spatial data can be treated as exactly or approximately exchangeable in a wide range of settings. In particular, under an infill asymptotic regime, we prove that the response values are, in a certain sense, locally approximately exchangeable for a broad class of spatial processes, and we develop a local spatial conformal prediction algorithm that yields valid prediction intervals without strong model assumptions like stationarity. Numerical examples with both real and simulated data confirm that the proposed conformal prediction intervals are valid and generally more efficient than existing model-based procedures for large datasets across a range of non-stationary and non-Gaussian settings.

Detecting localized damage in cantilevered structures under nonstationary ambient excitations via Gabor spectral mode transmissibility functions.

A method based on Gabor spectral mode transmissibility functions (GSMTFs) is proposed to detect local damage in a cantilevered structure under nonstationary ambient excitations. Gabor transformation and singular value decomposition are used to reduce the influences of other vibration modes on Gabor spectral mode transmissibility functions and process nonstationary structural responses, respectively. A new state characteristic based on the fundamental structure frequency is formulated on the basis of the GSMTFs, eventually leading to the development of a new damage indicator. The probability density functions of the damage indicator for healthy and damaged states can be estimated from the measured data, and the receiver operating characteristic (ROC) curve derived from these probability distributions and the corresponding area under the ROC curve (AUC) are used to determine the damage location. A six-degree-of-freedom system and a typical transmission tower are numerically studied, and the results show that the proposed method can estimate the structural damage location under nonstationary random loads. The proposed method is further validated with a planar frame in the laboratory, which exhibits multiple damage elements via random force hammer excitations. The results show that the AUC values computed for certain parts of the structure containing the damaged elements are greater than those for other parts of the structure, indicating the effectiveness of the proposed method. Moreover, the proposed method is compared with the dot product difference (DPD) index, and the results from the laboratory planar frame demonstrate that the proposed method can better identify damage.

Single-sensor rotating blade monitoring method under non-stationary conditions based on velocity and displacement.

A novel single-sensor method for monitoring rotating blade vibration is proposed and utilized to identify vibration parameters under the non-stationary condition. By analyzing the pulse-signal waveform, the blade tip displacement and vibration velocity are extracted. Then, the motion equation under the non-stationary condition is further developed to provide a theoretical basis. Finally, the optimization technology is applied to extract vibration parameters. Compared with multiple-sensor methods, the proposed method has lower installation difficulty, less equipment cost, fewer sensors, and no strict sensor layout requirement. Numerical simulations and experiments are conducted to validate the effectiveness and robustness of the proposed method. The relative error in the natural frequency does not exceed 0.1 %. Additionally, errors in other parameters are less than 8 % in the experiment.

Nonlinear Heart Rate Variability Analysis for Sleep Stage Classification Using Integration of Ballistocardiogram and Apple Watch.

Purpose: Wearable or non-contact, non-intrusive devices present a practical alternative to traditional polysomnography (PSG) for daily assessment of sleep quality. Physiological signals have been known to be nonlinear and nonstationary as the body adapts to states of rest or activity. By integrating more sophisticated nonlinear methodologies, the accuracy of sleep stage identification using such devices can be improved. This advancement enables individuals to monitor and adjust their sleep patterns more effectively without visiting sleep clinics. Patients and Methods: Six participants slept for three cycles of at least three hours each, wearing PSG as a reference, along with an Apple Watch, an actigraphy device, and a ballistocardiography (BCG) bed sensor. The physiological signals were processed with nonlinear methods and trained with a long short-term memory (LSTM) model to classify sleep stages. Nonlinear methods, such as return maps with advanced techniques to analyze the shape and asymmetry in physiological signals, were used to relate these signals to the autonomic nervous system (ANS). The changing dynamics of cardiac signals in restful or active states, regulated by the ANS, were associated with sleep stages and quality, which were measurable. Results: Approximately 73% agreement was obtained by comparing the combination of the BCG and Apple Watch signals against a PSG reference system to classify rapid eye movement (REM) and non-REM sleep stages. Conclusion: Utilizing nonlinear methods to evaluate cardiac dynamics showed an improved sleep quality detection with the non-intrusive devices in this study. A system of non-intrusive devices can provide a comprehensive outlook on health by regularly measuring sleeping patterns and quality over time, offering a relatively accessible method for participants. Additionally, a non-intrusive system can be integrated into a user's or clinic's bedroom environment to measure and evaluate sleep quality without negatively impacting sleep. Devices placed around the bedroom could measure user vitals over longer periods with minimal interaction from the user, representing their natural sleeping trends for more accurate health and sleep disorder diagnosis.

Robust adaptive deep brain stimulation control of in-silico non-stationary Parkinsonian neural oscillatory dynamics.

Objective. Closed-loop deep brain stimulation (DBS) is a promising therapy for Parkinson's disease (PD) that works by adjusting DBS patterns in real time from the guidance of feedback neural activity. Current closed-loop DBS mainly uses threshold-crossing on-off controllers or linear time-invariant (LTI) controllers to regulate the basal ganglia (BG) Parkinsonian beta band oscillation power. However, the critical cortex-BG-thalamus network dynamics underlying PD are nonlinear, non-stationary, and noisy, hindering accurate and robust control of Parkinsonian neural oscillatory dynamics.Approach. Here, we develop a new robust adaptive closed-loop DBS method for regulating the Parkinsonian beta oscillatory dynamics of the cortex-BG-thalamus network. We first build an adaptive state-space model to quantify the dynamic, nonlinear, and non-stationary neural activity. We then construct an adaptive estimator to track the nonlinearity and non-stationarity in real time. We next design a robust controller to automatically determine the DBS frequency based on the estimated Parkinsonian neural state while reducing the system's sensitivity to high-frequency noise. We adopt and tune a biophysical cortex-BG-thalamus network model as an in-silico simulation testbed to generate nonlinear and non-stationary Parkinsonian neural dynamics for evaluating DBS methods.Main results. We find that under different nonlinear and non-stationary neural dynamics, our robust adaptive DBS method achieved accurate regulation of the BG Parkinsonian beta band oscillation power with small control error, bias, and deviation. Moreover, the accurate regulation generalizes across different therapeutic targets and consistently outperforms current on-off and LTI DBS methods.Significance. These results have implications for future designs of closed-loop DBS systems to treat PD.

Sparse Wasserstein stationary subspace analysis for fault detection and diagnosis of nonstationary industrial processes.

Fault detection and diagnosis of nonstationary processes are crucial for ensuring the safety of industrial production systems. However, the nonstationarity of process data poses multifaceted challenges to them. First, conventional stationary fault detection methods encounter difficulties in discerning evolving trends within nonstationary data. Secondly, the majority of current nonstationary fault detection methods directly extract features from all variables, rendering them susceptible to redundant interference. Moreover, nonstationary trends possess the capacity to conceal and modify the correlations among variables. Coupled with the smearing effect of faults, it is challenging to achieve accurate fault diagnosis. To address these challenges, this paper proposes sparse Wasserstein stationary subspace analysis (SWSSA). Specifically, a ℓ2,p-norm constraint is introduced to endow the stationary subspace model with excellent sparse representation capability. Furthermore, recognizing that fault variables within the sparse stationary subspace influence only a limited subset of stationary sources, this paper proposes a novel contribution analysis method based on local dynamic preserving projection (LDPP), termed LDPPBC, which can effectively mitigate the smearing effect on nonstationary fault diagnosis. LDPPBC establishes a LDPP matrix by extracting the latent positional information of fault variables within the stationary subspace. This allows LDPPBC to selectively analyze the contributions of variables within the latent fault subspace to achieve precise fault diagnosis while avoiding the interference of variable contributions from the fault-free subspace. Finally, the superiority of the proposed method is thoroughly validated through a numerical simulation, a continuous stirred tank reactor, and a real industrial roaster.

Quantitative Detection of Vertical Track Irregularities under Non-Stationary Conditions with Variable Vehicle Speed.

Track irregularities directly affect the quality and safety of railway vehicle operations. Quantitative detection and real-time monitoring of track irregularities are of great importance. However, due to the frequent variable vehicle speed, vehicle operation is a typical non-stationary process. The traditional signal analysis methods are unsuitable for non-stationary processes, making the quantitative detection of the wavelength and amplitude of track irregularities difficult. To solve the above problems, this paper proposes a quantitative detection method of track irregularities under non-stationary conditions with variable vehicle speed by order tracking analysis for the first time. Firstly, a simplified wheel-rail dynamic model is established to derive the quantitative relationship between the axle-box vertical vibration and the track vertical irregularities. Secondly, the Simpson double integration method is proposed to calculate the axle-box vertical displacement based on the axle-box vertical acceleration, and the process error is optimized. Thirdly, based on the order tracking analysis theory, the angular domain resampling is performed on the axle-box vertical displacement time-domain signal in combination with the wheel rotation speed signals, and the quantitative detection of the track irregularities is achieved. Finally, the proposed method is validated based on simulation and field test analysis cases. We provide theoretical support and method reference for the quantitative detection method of track irregularities.

Identifying Characteristic Fire Properties with Stationary and Non-Stationary Fire Alarm Systems.

The article reviews issues associated with the operation of stationary and non-stationary electronic fire alarm systems (FASs). These systems are employed for the fire protection of selected buildings (stationary) or to monitor vast areas, e.g., forests, airports, logistics hubs, etc. (non-stationary). An FAS is operated under various environmental conditions, indoor and outdoor, favourable or unfavourable to the operation process. Therefore, an FAS has to exhibit a reliable structure in terms of power supply and operation. To this end, the paper discusses a representative FAS monitoring a facility and presents basic tactical and technical assumptions for a non-stationary system. The authors reviewed fire detection methods in terms of fire characteristic values (FCVs) impacting detector sensors. Another part of the article focuses on false alarm causes. Assumptions behind the use of unmanned aerial vehicles (UAVs) with visible-range cameras (e.g., Aviotec) and thermal imaging were presented for non-stationary FASs. The FAS operation process model was defined and a computer simulation related to its operation was conducted. Analysing the FAS operation process in the form of models and graphs, and the conducted computer simulation enabled conclusions to be drawn. They may be applied for the design, ongoing maintenance and operation of an FAS. As part of the paper, the authors conducted a reliability analysis of a selected FAS based on the original performance tests of an actual system in operation. They formulated basic technical and tactical requirements applicable to stationary and mobile FASs detecting the so-called vast fires.

EEG dynamic source imaging using a regularized optimization with spatio-temporal constraints.

One of the most important needs in neuroimaging is brain dynamic source imaging with high spatial and temporal resolution. EEG source imaging estimates the underlying sources from EEG recordings, which provides enhanced spatial resolution with intrinsically high temporal resolution. To ensure identifiability in the underdetermined source reconstruction problem, constraints on EEG sources are essential. This paper introduces a novel method for estimating source activities based on spatio-temporal constraints and a dynamic source imaging algorithm. The method enhances time resolution by incorporating temporal evolution of neural activity into a regularization function. Additionally, two spatial regularization constraints based on L 1 and L 2 norms are applied in the transformed domain to address both focal and spread neural activities, achieved through spatial gradient and Laplacian transform. Performance evaluation, conducted quantitatively using synthetic datasets, discusses the influence of parameters such as source extent, number of sources, correlation level, and SNR level on temporal and spatial metrics. Results demonstrate that the proposed method provides superior spatial and temporal reconstructions compared to state-of-the-art inverse solutions including STRAPS, sLORETA, SBL, dSPM, and MxNE. This improvement is attributed to the simultaneous integration of transformed spatial and temporal constraints. When applied to a real auditory ERP dataset, our algorithm accurately reconstructs brain source time series and locations, effectively identifying the origins of auditory evoked potentials. In conclusion, our proposed method with spatio-temporal constraints outperforms the state-of-the-art algorithms in estimating source distribution and time courses.

Non-stationary Bayesian spatial model for disease mapping based on sub-regions.

This paper aims to extend the Besag model, a widely used Bayesian spatial model in disease mapping, to a non-stationary spatial model for irregular lattice-type data. The goal is to improve the model's ability to capture complex spatial dependence patterns and increase interpretability. The proposed model uses multiple precision parameters, accounting for different intensities of spatial dependence in different sub-regions. We derive a joint penalized complexity prior to the flexible local precision parameters to prevent overfitting and ensure contraction to the stationary model at a user-defined rate. The proposed methodology can be used as a basis for the development of various other non-stationary effects over other domains such as time. An accompanying R package fbesag equips the reader with the necessary tools for immediate use and application. We illustrate the novelty of the proposal by modeling the risk of dengue in Brazil, where the stationary spatial assumption fails and interesting risk profiles are estimated when accounting for spatial non-stationary. Additionally, we model different causes of death in Brazil, where we use the new model to investigate the spatial stationarity of these causes.

Assessing the role of cold front passage and synoptic patterns on air pollution in the Korean Peninsula.

Various numerical experiments using WRF (Weather Research & Forecasting Model) and CMAQ (Community Multiscale Air Quality Modeling System) were performed to analyze the phenomenon of rapidly high concentration PM2.5 after the passage of a cold front in an area with limited local emissions. The episode period was from January 14 to 23, 2018, and analysis was conducted by dividing it into two stages according to the characteristics of changes in PM2.5 concentrations during the period. Through the analysis of observational data during the episode period, we confirmed meteorological impacts (decrease in temperature, increase in wind speed and relative humidity) and an increase in air pollution (PM10 and PM2.5) attributed to the passage of a cold front. Using CMAQ's IPR (Integrated Process Rate) analysis, the contribution of the horizontal advection process was observed in transporting PM2.5 to Gangneung at higher altitudes, and the PM2.5 concentrations at the surface increased because the vertical advection process was influenced by the terrain. Notably, in Stage 2 (64 µg·m-3), a higher contribution of the vertical advection process compared to Stage 1 (35 µg·m-3) was observed, which is attributed to the differences in synoptic patterns following the passage of the cold front. During Stage 2, following the cold front, atmospheric stability (dominance of high-pressure system) led to air subsidence and the presence of a temperature inversion layer, creating favorable meteorological conditions for the accumulation of air pollutants. This study offers the mechanisms of air pollution over the Korean Peninsula under non-stationary meteorological conditions, particularly in relation to the passage of the cold front (low-pressure system). Notably, the influence of a cold front can vary according to the synoptic patterns that develop following its passage.

Temporal self-attention for risk prediction from electronic health records using non-stationary kernel approximation.

Effective modeling of patient representation from electronic health records (EHRs) is increasingly becoming a vital research topic. Yet, modeling the non-stationarity in EHR data has received less attention. Most existing studies follow a strong assumption of stationarity in patient representation from EHRs. However, in practice, a patient's visits are irregularly spaced over a relatively long period of time, and disease progression patterns exhibit non-stationarity. Furthermore, the time gaps between patient visits often encapsulate significant domain knowledge, potentially revealing undiscovered patterns that characterize specific medical conditions. To address these challenges, we introduce a new method which combines the self-attention mechanism with non-stationary kernel approximation to capture both contextual information and temporal relationships between patient visits in EHRs. To assess the effectiveness of our proposed approach, we use two real-world EHR datasets, comprising a total of 76,925 patients, for the task of predicting the next diagnosis code for a patient, given their EHR history. The first dataset is a general EHR cohort and consists of 11,451 patients with a total of 3,485 unique diagnosis codes. The second dataset is a disease-specific cohort that includes 65,474 pregnant patients and encompasses a total of 9,782 unique diagnosis codes. Our experimental evaluation involved nine prediction models, categorized into three distinct groups. Group 1 comprises the baselines: original self-attention with positional encoding model, RETAIN model, and LSTM model. Group 2 includes models employing self-attention with stationary kernel approximations, specifically incorporating three variations of Bochner's feature maps. Lastly, Group 3 consists of models utilizing self-attention with non-stationary kernel approximations, including quadratic, cubic, and bi-quadratic polynomials. The experimental results demonstrate that non-stationary kernels significantly outperformed baseline methods for NDCG@10 and Hit@10 metrics in both datasets. The performance boost was more substantial in dataset 1 for the NDCG@10 metric. On the other hand, stationary Kernels showed significant but smaller gains over baselines and were nearly as effective as Non-stationary Kernels for Hit@10 in dataset 2. These findings robustly validate the efficacy of employing non-stationary kernels for temporal modeling of EHR data, and emphasize the importance of modeling non-stationary temporal information in healthcare prediction tasks.

ANOPOW FOR REPLICATED NONSTATIONARY TIME SERIES IN EXPERIMENTS.

We propose a novel analysis of power (ANOPOW) model for analyzing replicated nonstationary time series commonly encountered in experimental studies. Based on a locally stationary ANOPOW Cramér spectral representation, the proposed model can be used to compare the second-order time-varying frequency patterns among different groups of time series and to estimate group effects as functions of both time and frequency. Formulated in a Bayesian framework, independent two-dimensional second-order random walk (RW2D) priors are assumed on each of the time-varying functional effects for flexible and adaptive smoothing. A piecewise stationary approximation of the nonstationary time series is used to obtain localized estimates of time-varying spectra. Posterior distributions of the time-varying functional group effects are then obtained via integrated nested Laplace approximations (INLA) at a low computational cost. The large-sample distribution of local periodograms can be appropriately utilized to improve estimation accuracy since INLA allows modeling of data with various types of distributions. The usefulness of the proposed model is illustrated through two real data applications: analyses of seismic signals and pupil diameter time series in children with attention deficit hyperactivity disorder. Simulation studies, Supplementary Materials (Li, Yue and Bruce, 2023a), and R code (Li, Yue and Bruce, 2023b) for this article are also available.

Evaluating flood potential in the Mahanadi River Basin, India, using Gravity Recovery and Climate Experiment (GRACE) data and topographic flood susceptibility index under non-stationary framework.

Extreme flood events have been recorded recently in the Mahanadi River basin in India with a high destructive potential that causes large social and economic damages. Because fewer hydrometeorological stations can record the flood magnitude in the basin, exploring new datasets like Gravity Recovery and Climate Experiment (GRACE) becomes important to overcome the barriers of assessing the hydrological extremes. The study estimates the flood potential using the GRACE-based terrestrial water storage (TWS) and analytical hierarchy process (AHP)-based topographic flood susceptibility to model the non-stationary flood frequency. During extreme flood events, the magnitude of the combined flood potential index (CFPI) is high (CFPI > 0.6), which correlates with higher river discharge. The CFPI value for the 2012 flood event with a discharge of 11,000 m3/sec (corresponds to a 35-year return period) is recorded at 0.67. Likewise, the CFPI for the flood event in 2011, which corresponds to a return period of 17 years, also stands at 0.63. The overall correlation between the discharge values of various flood events and CFPI values is above 0.8 for all locations, indicating GRACE-based CFPI's applicability for identifying the flood risk for larger basins like Mahanadi. Furthermore, on integrating CFPI as a covariate in non-stationary flood frequency modeling, the study found its superior performance when compared to both stationary models and non-stationary models with time or other climate indices as covariates, thus, helping in accurate estimation of flood return levels that are very useful in the hydrological design of water resources projects.

TCDformer: A transformer framework for non-stationary time series forecasting based on trend and change-point detection.

Although time series prediction models based on Transformer architecture have achieved significant advances, concerns have arisen regarding their performance with non-stationary real-world data. Traditional methods often use stabilization techniques to boost predictability, but this often results in the loss of non-stationarity, notably underperforming when tackling major events in practical applications. To address this challenge, this research introduces an innovative method named TCDformer (Trend and Change-point Detection Transformer). TCDformer employs a unique strategy, initially encoding abrupt changes in non-stationary time series using the local linear scaling approximation (LLSA) module. The reconstructed contextual time series is then decomposed into trend and seasonal components. The final prediction results are derived from the additive combination of a multilayer perceptron (MLP) for predicting trend components and wavelet attention mechanisms for seasonal components. Comprehensive experimental results show that on standard time series prediction datasets, TCDformer significantly surpasses existing benchmark models in terms of performance, reducing MSE by 47.36% and MAE by 31.12%. This approach offers an effective framework for managing non-stationary time series, achieving a balance between performance and interpretability, making it especially suitable for addressing non-stationarity challenges in real-world scenarios.

The non-stationary and spatially varying associations between hand, foot and mouth disease and multiple environmental factors: A Bayesian spatiotemporal mapping model study.

The transmission and prevalence of Hand, Foot and Mouth Disease (HFMD) are affected by a variety of natural and socio-economic environmental factors. This study aims to quantitatively investigate the non-stationary and spatially varying associations between various environmental factors and HFMD risk. We collected HFMD surveillance cases and a series of relevant environmental data from 2013 to 2021 in Xi'an, Northwest China. By controlling the spatial and temporal mixture effects of HFMD, we constructed a Bayesian spatiotemporal mapping model and characterized the impacts of different driving factors into global linear, non-stationary and spatially varying effects. The results showed that the impact of meteorological conditions on HFMD risk varies in both type and magnitude above certain thresholds (temperature: 30 °C, precipitation: 70 mm, solar radiation: 13000 kJ/m2, pressure: 945 hPa, humidity: 69%). Air pollutants (PM2.5, PM10, NO2) showed an inverted U-shaped relationship with the risk of HFMD, while other air pollutants (O3, SO2) showed nonlinear fluctuations. Moreover, the driving effect of increasing temperature on HFMD was significant in the 3-year period, while the inhibitory effect of increasing precipitation appeared evident in the 5-year period. In addition, the proportion of urban/suburban/rural area had a strong influence on HFMD, indicating that the incidence of HFMD firstly increased and then decreased during the rapid urbanization process. The influence of population density on HFMD was not only limited by spatial location, but also varied between high and low intervals. Higher road density inhibited the risk of HFMD, but higher night light index promoted the occurrence of HFMD. Our findings further demonstrated that both ecological and socioeconomic environmental factors can pose multiple driving effects on increasing the spatiotemporal risk of HFMD, which is of great significance for effectively responding to the changes in HFMD epidemic outbreaks.

Coordination as inference in multi-agent reinforcement learning.

The Centralized Training and Decentralized Execution (CTDE) paradigm, where a centralized critic is allowed to access global information during the training phase while maintaining the learned policies executed with only local information in a decentralized way, has achieved great progress in recent years. Despite the progress, CTDE may suffer from the issue of Centralized-Decentralized Mismatch (CDM): the suboptimality of one agent's policy can exacerbate policy learning of other agents through the centralized joint critic. In contrast to centralized learning, the cooperative model that most closely resembles the way humans cooperate in nature is fully decentralized, i.e. Independent Learning (IL). However, there are still two issues that need to be addressed before agents coordinate through IL: (1) how agents are aware of the presence of other agents, and (2) how to coordinate with other agents to improve joint policy under IL. In this paper, we propose an inference-based coordinated MARL method: Deep Motor System (DMS). DMS first presents the idea of individual intention inference where agents are allowed to disentangle other agents from their environment. Secondly, causal inference was introduced to enhance coordination by reasoning each agent's effect on others' behavior. The proposed model was extensively experimented on a series of Multi-Agent MuJoCo and StarCraftII tasks. Results show that the proposed method outperforms independent learning algorithms and the coordination behavior among agents can be learned even without the CTDE paradigm compared to the state-of-the-art baselines including IPPO and HAPPO.

Hilbert transform for covariance analysis of periodically nonstationary random signals with high-frequency modulation.

We discuss the use of the Hilbert transform for the analysis of periodically non-stationary random signals (PNRSs), whose carrier harmonics are modulated by jointly stationary high-frequency narrow-band random processes. PNRS of this type are suitable models for numerous natural and man-made phenomena, including the vibration of a damaged mechanism. We show that the auto-covariance function of the signal and its Hilbert transform are the same, and that their cross-covariance functions differ only in their sign, meaning that the sum of squares of the signal and its Hilbert transform cannot be considered a 'squared envelope' and no new information is contained compared with the variance of the raw signal. A representation of the signal in the form of a superposition of high-frequency components is obtained and it is shown that these components are jointly periodically non-stationary random processes. The properties of the band-pass filtered signals are examined, and it is shown that band-pass filtering can reduce both the number of signal variance cyclic harmonics and their amplitudes. We show that it is possible to extract the quadratures of narrow-band high-frequency modulation processes using the Hilbert transform. The results obtained here theoretically substantiate the use of the Hilbert transform for the analysis of high-frequency modulation which occurs when a fault appears. They offer a new way to consider the traditional approach to vibration diagnosis. A processing technique that can be considered an alternative to envelope analysis is described, and its use in the analysis of a vibration signal is discussed.

Non-Stationary Dynamic Mode Decomposition.

Many physical processes display complex high-dimensional time-varying behavior, from global weather patterns to brain activity. An outstanding challenge is to express high dimensional data in terms of a dynamical model that reveals their spatiotemporal structure. Dynamic Mode Decomposition is a means to achieve this goal, allowing the identification of key spatiotemporal modes through the diagonalization of a finite dimensional approximation of the Koopman operator. However, these methods apply best to time-translationally invariant or stationary data, while in many typical cases, dynamics vary across time and conditions. To capture this temporal evolution, we developed a method, Non-Stationary Dynamic Mode Decomposition, that generalizes Dynamic Mode Decomposition by fitting global modulations of drifting spatiotemporal modes. This method accurately predicts the temporal evolution of modes in simulations and recovers previously known results from simpler methods. To demonstrate its properties, the method is applied to multi-channel recordings from an awake behaving non-human primate performing a cognitive task.

Multifractal detrended fluctuation analysis of insole pressure sensor data to diagnose vestibular system disorders.

The vestibular system (VS) is a sensory system that has a vital function in human life by serving to maintain balance. In this study, multifractal detrended fluctuation analysis (MFDFA) is applied to insole pressure sensor data collected from subjects in order to extract features to identify diseases related to VS dysfunction. We use the multifractal spectrum width as the feature to distinguish between healthy and diseased people. It is observed that multifractal behavior is more dominant and thus the spectrum is wider for healthy subjects, where we explain the reason as the long-range correlations of the small and large fluctuations of the time series for this group. We directly process the instantaneous pressure values to extract features in contrast to studies in the literature where gait analysis is based on investigation of gait dynamics (stride time, stance time, etc.) requiring long walking time. Thus, as the main innovation of this work, we detrend the data to give meaningful information even for a relatively short walk. Extracted feature set was input to fundamental classification algorithms where the Support-Vector-Machine (SVM) performed best with an average accuracy of 98.2% for the binary classification as healthy or suffering. This study is a substantial part of a big project where we finally aim to identify the specific VS disease that causes balance disorder and also determine the stage of the disease, if any. Within this scope, the achieved performance gives high motivation to work more deeply on the issue.