Dynamic Time Research Articles

The recurrent temporal restricted Boltzmann machine captures neural assembly dynamics in whole-brain activity

Animal behaviour alternates between stochastic exploration and goal-directed actions, which are generated by the underlying neural dynamics. Previously, we demonstrated that the compositional Restricted Boltzmann Machine (cRBM) can decompose whole-brain activity of larval zebrafish data at the neural level into a small number (∼100-200) of assemblies that can account for the stochasticity of the neural activity (van der Plas et al., eLife, 2023). Here, we advance this representation by extending to a combined stochastic-dynamical representation to account for both aspects using the recurrent temporal RBM (RTRBM) and transfer-learning based on the cRBM estimate. We demonstrate that the functional advantage of the RTRBM is captured in the temporal weights on the hidden units, representing neural assemblies, for both simulated and experimental data. Our results show that the temporal expansion outperforms the stochastic-only cRBM in terms of generalization error and achieves a more accurate representation of the moments in time. Lastly, we demonstrate that we can identify the original time-scale of assembly dynamics by estimating multiple RTRBMs at different temporal resolutions. Together, we propose that RTRBMs are a valuable tool for capturing the combined stochastic and time-predictive dynamics of large-scale data sets.

The recurrent temporal restricted Boltzmann machine captures neural assembly dynamics in whole-brain activity.

Animal behaviour alternates between stochastic exploration and goal-directed actions, which are generated by the underlying neural dynamics. Previously, we demonstrated that the compositional Restricted Boltzmann Machine (cRBM) can decompose whole-brain activity of larval zebrafish data at the neural level into a small number (∼100-200) of assemblies that can account for the stochasticity of the neural activity (van der Plas et al., eLife, 2023). Here, we advance this representation by extending to a combined stochastic-dynamical representation to account for both aspects using the recurrent temporal RBM (RTRBM) and transfer-learning based on the cRBM estimate. We demonstrate that the functional advantage of the RTRBM is captured in the temporal weights on the hidden units, representing neural assemblies, for both simulated and experimental data. Our results show that the temporal expansion outperforms the stochastic-only cRBM in terms of generalization error and achieves a more accurate representation of the moments in time. Lastly, we demonstrate that we can identify the original time-scale of assembly dynamics by estimating multiple RTRBMs at different temporal resolutions. Together, we propose that RTRBMs are a valuable tool for capturing the combined stochastic and time-predictive dynamics of large-scale data sets.

Dynamic signatures: a mathematical approach to analysis

Abstract This study evaluates mathematical tools (principal component analysis, dynamic time warping, and the Kolmogorov–Smirnov hypothesis test) to analyse global and local data from dynamic signatures to reduce subjectivity and increase the reproducibility of handwriting examination using a two-step approach. A data set composed of 1800 genuine signature samples, 870 simulated signatures, and 60 disguises (30 formally similar or ‘autosimulated’ and 30 random but different from usual) provided by 30 volunteers was collected. The first step involved global data analysis using principal component analysis and a hypothesis test performed for 62 global characteristics, and associations of these characteristics were analysed through calculations of multivariate distance followed by a hypothesis test. The second step involved the analysis of local characteristics including vertical and horizontal positions, speed, pressure gradient, acceleration, and jerk point-to-point, by using dynamic time warping followed by a hypothesis test. Optimization of sensitivity and specificity metrics of the hypothesis test was explored by varying its stringency and observing accuracy rates for the simulated and genuine groups. A P-value threshold of 1 × 10−10 was found to be optimal, making the test more restrictive and yielding accuracy rates of 96.7% for genuine global data and 88.9% for simulated data. The same cutoff value for local characteristics provided an average accuracy rate of 95.4% for genuine samples and 94.7% for simulated samples, demonstrating high accuracy for both simulated and genuine samples. However, the method did not offer reasonable accuracy rates for disguises, consistent with observations in traditional handwriting examination. Our approach provided satisfactory results for forensic examination use. The visualization of graphs and signatures and analysis of all identifying elements of handwriting by the examining expert are still essential. In future studies, we plan to perform blind tests to validate our approach and propose a rigorous methodology.

Defining Stable Phases of Open Quantum Systems

The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors of the non-Hermitian operators that generate the dynamics, i.e., quantum channels (Markov chains). However, since these operators are non-Hermitian, their spectra are an unreliable guide to dynamical relaxation timescales or to stability against perturbations. We propose an alternative dynamical criterion for a steady state to be in a stable phase, which we name uniformity: Informally, our criterion amounts to requiring that, under sufficiently small local perturbations of the dynamics, the unperturbed and perturbed steady states are related to one another by a finite-time dissipative evolution. We show that this criterion implies many of the properties one would want from any reasonable definition of a phase. We prove that uniformity is satisfied in a canonical classical cellular automaton, and we provide numerical evidence that the gap determines the relaxation rate between nearby steady states in the same phase, a situation we conjecture holds generically whenever uniformity is satisfied. We further conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability. Published by the American Physical Society 2024

IMITASD: Imitation Assessment Model for Children with Autism Based on Human Pose Estimation

Autism is a challenging brain disorder affecting children at global and national scales. Applied behavior analysis is commonly conducted as an efficient medical therapy for children. This paper focused on one paradigm of applied behavior analysis, imitation, where children mimic certain lessons to enhance children’s social behavior and play skills. This paper introduces IMITASD, a practical monitoring assessment model designed to evaluate autistic children’s behaviors efficiently. The proposed model provides an efficient solution for clinics and homes equipped with mid-specification computers attached to webcams. IMITASD automates the scoring of autistic children’s videos while they imitate a series of lessons. The model integrates two core modules: attention estimation and imitation assessment. The attention module monitors the child’s position by tracking the child’s face and determining the head pose. The imitation module extracts a set of crucial key points from both the child’s head and arms to measure the similarity with a reference imitation lesson using dynamic time warping. The model was validated using a refined dataset of 268 videos collected from 11 Egyptian autistic children during conducting six imitation lessons. The analysis demonstrated that IMITASD provides fast scoring, takes less than three seconds, and shows a robust measure as it has a high correlation with scores given by medical therapists, about 0.9, highlighting its effectiveness for children’s training applications.

Revised Cross-Correlation and Time-Lag between Cosmic Ray Intensity and Solar Activity Using Chatterjee’s Correlation Coefficient

This study revisits the cross-correlation between cosmic ray intensity (CRI) and solar activity (SA) by comparing traditional Pearson correlation with Chatterjee’s correlation coefficient. Traditional analyses using Pearson correlation are useful for identifying linear relationships and time lags. However, they may not fully capture more complex interactions in the data. Chatterjee’s correlation coefficient, while sensitive to different types of relationships, including nonlinear ones, provides a complementary perspective on the temporal relationships between CRI and SA. This approach broadens our understanding of potential dependencies, offering additional insights that may not be captured through Pearson correlation alone.The findings reveal that Chatterjee’s correlation complements Pearson’s insights by providing an alternative view of the relationship between cosmic ray intensity (CRI) and solar activity (SA). The results show that Chatterjee’s correlation coefficients are, on average, approximately 45-50% smaller than Pearson’s, which could reflect different sensitivities to the underlying data structure rather than solely indicating a nonlinear component. Additionally, the time lags identified using Chatterjee’s correlation are generally shorter and more consistent across different solar cycles compared to those obtained with Pearson’s correlation, suggesting that CCC may capture temporal patterns in a distinct manner.Further analysis using Dynamic Time Warping (DTW) and Mean Absolute Percentage Error (MAPE) metrics demonstrated that, in more than half of the scenarios considered, alignment based on Chatterjee’s time lags resulted in lower errors and better alignment of the series compared to Pearson’s lags. This indicates that Chatterjee’s method is particularly effective for capturing the immediate and nuanced responses of CRI to SA changes, especially in recent solar cycles.This comprehensive approach provides broader insights into the dynamic interactions between cosmic ray intensity (CRI) and solar activity (SA), highlighting the importance of considering multiple correlation measures, including both linear and nonlinear approaches, in space weather research. The results suggest that Chatterjee’s correlation offers a complementary perspective on these interactions, providing additional details about how SA influences CRI over time, which may not be fully captured by Pearson’s correlation alone.

Seasonality of common respiratory viruses: Analysis of nationwide time-series data.

Understanding the seasonal behaviours of respiratory viruses is crucial for preventing infections. We evaluated the seasonality of respiratory viruses using time-series analyses. This study analysed prospectively collected nationwide surveillance data on eight respiratory viruses, gathered from the Korean Influenza and Respiratory Surveillance System. The data were collected on a weekly basis by 52 nationwide primary healthcare institutions between 2015 and 2019. We performed Spearman correlation analyses, similarity analyses via dynamic time warping (DTW) and seasonality analyses using seasonal autoregressive integrated moving average (SARIMA). The prevalence of rhinovirus (RV, 23.6%-31.4%), adenovirus (AdV, 9.2%-16.6%), human coronavirus (HCoV, 3.0%-6.6%), respiratory syncytial virus (RSV, 11.7%-20.1%), influenza virus (IFV, 11.7%-21.5%), parainfluenza virus (PIV, 9.2%-12.6%), human metapneumovirus (HMPV, 5.6%-6.9%) and human bocavirus (HBoV, 5.0%-6.4%) were derived. Most of them exhibited a high positive correlation in Spearman analyses. In DTW analyses, all virus data from 2015 to 2019, except AdV, exhibited good alignments. In SARIMA, AdV and RV did not show seasonality. Other viruses showed 12-month seasonality. We describe the viruses as winter viruses (HCoV, RSV and IFV), spring/summer viruses (PIV, HBoV), a spring virus (HMPV) and all-year viruses with peak incidences during school periods (RV and AdV). This is the first study to comprehensively analyse the seasonal behaviours of the eight most common respiratory viruses using nationwide, prospectively collected, sentinel surveillance data.

Identify and map coastal aquaculture ponds and their drainage and impoundment dynamics

Sustainable management of coastal aquaculture ponds could achieve win-win between food and economic benefits and ecological conservation including waterbird. In this study, 5,790 Harmonized Landsat and Sentinel-2 images from July 2021 to June 2022 and 498 Sentinel-1 images from July 2021, August 2021, and June 2022 as supplementary data were collected to calculate multiple water indices. Based on Otsu algorithm to distinguish between water and non-water region and Savitzky-Golay filtering to optimize time series, coastal aquaculture ponds were identified using the SNIC. Furthermore, their drainage and impoundment phases were determined using the Dynamic Time Warping-Kmeans++ method. Finally, a new 30-m resolution dataset at the national scale of China was generated with an overall accuracy greater than 90 % for both the pond map and the drainage and impoundment phases. Our observations revealed that the total area was 7,919.53 km2, with the largest pond area in Shandong Province. Among the coastal aquaculture ponds, 27.95 % were seasonal aquaculture ponds, 70.32 % were yearlong aquaculture ponds, and 1.49 % were abandoned aquaculture ponds. Drainage start dates, end dates, and durations were calculated based on abrupt changes in the water proportion time series. Drainage start dates were concentrated from September to December, while drainage end dates were from January to April. Drainage durations of coastal aquaculture ponds ranged from two weeks to six months, with Shanghai Municipality having the longest drainage durations and Taiwan Province having the shortest drainage durations. The findings could provide scientific support for modifying the drainage and impoundment phases of coastal aquaculture ponds to achieve the win–win goal of improving economic development and protecting waterbirds or improving offshore water quality.

A Merger-driven Scenario for Clumpy Galaxy Formation in the Epoch of Reionization: Physical Properties of Clumps in the FirstLight Simulation

Recent JWST observations with superb angular resolution have revealed the existence of clumpy galaxies at high redshift through the detection of rest-frame optical emission lines. We use the FirstLight simulation to study the properties of (sub)galactic clumps that are bright in the [O III] λ5007 line with flux greater than ∼10−18 erg s−1 cm−2, to be detected by JWST. For 62 simulated galaxies that have stellar masses of (0.5–6) × 1010 M ⊙ at z = 5, we find clumps in 1828 snapshots in the redshift range z = 9.5–5.5. The clumps are identified by the surface density of the star formation rate (SFR). About one-tenth of the snapshots show the existence of clumpy systems with two or more components. Most of the clumps are formed by mergers and can be characterized by their ages: central clumps dominated by stellar populations older than 50 Myr, and off-centered clumps dominated by younger stellar populations with specific SFRs of ∼50 Gyr−1. The latter type of young clumps is formed from gas debris in the tidal tails of major mergers with baryonic mass ratios of 1 ≤ q < 4. The merger-induced clumps are short-lived and merge within a dynamical time of several tens of million years. The number density of the clumpy systems is estimated to be ∼10−5 cMpc−3, which is large enough to be detected in recent JWST surveys.

Human-Robot Interactive Skill Learning and Correction for Polishing Based on Dynamic Time Warping Iterative Learning Control

Human-Robot Interactive Skill Learning and Correction for Polishing Based on Dynamic Time Warping Iterative Learning Control

Break a peg! A study of stablecoin co-instability

Following the increasing adoption of stablecoins, their robustness has become an ongoing concern for investors and regulators alike. This article studies the co-instability of a large panel of stablecoins by identifying their structural breaks and co-occurrences. Moreover, we use Dynamic Time Warping (DTW) and Dynamic Conditional Correlation DCC-GARCH models to assess spillover effects in the wake of four major black swan events in the crypto world. Similar to prior literature, we conclude that algorithmic stablecoins were the major shock receivers of the IRON TITAN and TERRA LUNA crashes, highlighting the importance of allowing for sufficient margins of safety in their design. We also observe that the FTX bankruptcy and the Silicon Valley Bank collapse had repercussions of a different nature and affected more categories of stablecoins, from algorithmic to fiat money-backed. We also highlight how, irrespective of the idiosyncratic or systemic nature of the shocks, well-known custodial stablecoins, as well as the most successful crypto-collateralized tokens, showed resilience during or in the immediate aftermath of these events.

Machine learning-based estimation of respiratory fluctuations in a healthy adult population using resting state BOLD fMRI and head motion parameters.

External physiological monitoring is the primary approach to measure and remove effects of low-frequency respiratory variation from BOLD-fMRI signals. However, the acquisition of clean external respiratory data during fMRI is not always possible, so recent research has proposed using machine learning to directly estimate respiratory variation (RV), potentially obviating the need for external monitoring. In this study, we propose an extended method for reconstructing RV waveforms directly from resting state BOLD-fMRI data in healthy adult participants with the inclusion of both BOLD signals and derived head motion parameters. In the proposed method, 1D convolutional neural networks (1D-CNNs) used BOLD signals and head motion parameters to reconstruct the RV waveform for the whole fMRI scan time. Resting-state fMRI data and associated respiratory records from the Human Connectome Project in Young Adults (HCP-YA) dataset are used to train and test the proposed method. Compared to using only BOLD-fMRI data for a CNN input, this approach yielded improvements of 14% in mean absolute error, 24% in mean square error, 14% in correlation, and 12% in dynamic time warping. When tested on independent datasets, the method demonstrated generalizability, even in data with different TRs and physiological conditions. This study shows that the respiratory variations could be reconstructed from BOLD-fMRI data in the young adult population, and its accuracy could be improved using supportive data such as head motion parameters. The method also performed well on independent datasets with different experimental conditions.

Transfer learning and source domain restructuring-based BiLSTM approach for building energy consumption prediction

ABSTRACT Currently, building energy consumption prediction typically relies on vast amounts of historical data. However, for newly constructed buildings, the scarcity of data leads to reduced prediction accuracy. To address this challenge, this paper proposes a novel approach that integrates transfer learning with a source domain reconstruction-based BiLSTM model for building energy consumption prediction. In the first stage, both source and target domains are clustered into profile types using k-means. For each profile type in the target domain, the most similar profiles in the source domain are identified using Maximum Mean Discrepancy and Dynamic Time Warping. The source domain is then reconstructed by combining these identified profiles based on their proportions in the target domain. Subsequently, a feature extraction method based on EMD-CWT-Conv is introduced. Empirical Mode Decomposition is first applied to decompose and filter the source domain data. Continuous Wavelet Transform is then employed to extract distinctive frequency-domain and time-domain features from both the reconstructed source domain and the target domain. Final predictions are made using transfer learning and fine-tuning. Experiments on a grocery shop and a school show that the proposed approach reduces Mean Absolute Percentage Error by at least 13.19% and 17.67%, respectively.

Comparison of SEMG-Based Hand Gesture Classifiers

Machine learning techniques have shown success in classifying hand gestures. As the prevalence of prosthetic devices continues to rise, the adoption of non-invasive technologies, such as surface electromyography (sEMG), becomes paramount. This study systematically assesses the isolated influence of classification algorithms within hand gesture recognition (HGR) systems using sEMG data and dynamic time warping (DTW) based features. This approach effectively handles temporal variations in sEMG signals by leveraging DTW, ensuring input features are invariant to gesture speed. Six supervised learning classifiers were evaluated: the multilayer perceptron, support vector machine, logistic regression, linear discriminant analysis, k-nearest neighbors, and decision tree. Cross-validation was employed to fine-tune the segmentation hyperparameters, significantly improving results. To ensure reproducibility, the source code has been made available, the proposed system design has been detailed, and the evaluation protocols have been described. Our findings indicate that logistic regression outperformed other classifiers in this setup, achieving 95.2% accuracy in classifying six hand movements from ten healthy individuals, representing a 1.6% improvement over the best previously reported performance using the same publicly available dataset. Future research will assess the proposed HGR system’s generalization capability on larger datasets suitable for training more complex classifiers, including deep learning models.

The Meissner effect in neutron stars

Abstract We present the first model aimed at understanding how the Meissner effect in a young neutron star affects its macroscopic magnetic field. In this model, field expulsion occurs on a dynamical timescale, and is realised through two processes that occur at the onset of superconductivity: fluid motions causing the dragging of field lines, followed by magnetic reconnection. Focussing on magnetic fields weaker than the superconducting critical field, we show that complete Meissner expulsion is but one of four possible generic scenarios for the magnetic-field geometry, and can never expel magnetic flux from the centre of the star. Reconnection causes the release of up to ∼5 × 1046 erg of energy at the onset of superconductivity, and is only possible for certain favourable early-phase dynamics and for pre-condensation fields 1012 G ≲ B ≲ 5 × 1014 G. Fields weaker or stronger than this are predicted to thread the whole star.

Non-elastic time series fuzzy clustering for efficient analysis of industrial data sets

In line with the green transition and digitalization trends, there is an increasing need for effective performance and health monitoring of production machines. Machine operation footprints resonate in quantities such as supply current and pneumatic line pressure, providing valuable insights when analyzed. Examining these low-level signals allows for monitoring and identification of changes in machine operation over time. A critical step in analyzing machine data is clustering, requiring an effective method for calculating time series cluster centroids. This paper introduces Error in Aligned series (ERAL), a novel method that generates a time series centroid that distills the fundamental shape of the underlying datasets. ERAL employs a fuzzy clustering-inspired iterative process for temporal alignment and averaging, avoiding the pathological artifacts often introduced by popular time-warping methods. Our analysis shows that existing methods can create artificial spikes and plateaus, which ERAL mitigates; it remains faithful to the original data shape. Additionally, ERAL offers improvements in computational efficiency and prototype quality. We evaluate the method against Dynamic Time Warping (DTW)-based methods across various datasets, and apply it to a time series clustering task using a real-world industrial dataset. In combination with a fuzzy clustering algorithm, ERAL generates visually convincing clusters. By leveraging fuzzy membership concepts, it achieves robust and adaptable clustering outcomes that reflect real-world data complexity and ambiguity.

Differences in Changes of Mobility Patterns Across the Globe—Evidence From a Natural Experiment

ABSTRACTThe impact of population mobility and transportation choices on the environment is significant. Sustainable mobility policies require an understanding of evolving mobility patterns. This study examines global mobility variations across countries using COVID‐19 Community Mobility Reports. Employing the k‐medoids algorithm and Dynamic Time Warping, we analyzed mobility dynamics. Results reveal diverse changes in population mobility. Around 52 Global North countries exhibit approximately 10% reduction in professional activity‐related traffic post‐COVID‐19. Regarding urban green space mobility, only 29 countries exhibit strong seasonality, with summer traffic in the northern hemisphere peaking at about 150% higher than winter traffic. Three groups of countries are identified concerning public transport mobility: returning to pre‐pandemic levels, experiencing a 25% increase, and nearly doubling from pre‐pandemic levels. This underscores the key determinants for sustainable mobility policy implementation. Fifteen highly developed countries share similar mobility patterns across six areas studied, facilitating the exchange of sustainable mobility solutions and best practices. This research underscores the importance of understanding and addressing evolving mobility patterns for effective environmental policy planning.

Performing Dynamic Analysis of the Conceret Structures using Genetic Algorithm and Determining the Optimal Range during a Natural Hazard Crisis (Tempe, Arizona, USA)

The approach employs a binary genetic algorithm alongside natural numbers. Given the differences between accelerometers and scale coefficients, the genetic algorithm introduced herein is a hybrid, featuring two chromosomes. A key factor influencing the accuracy and effectiveness of these programs is the precise estimation of their parameters. When these parameters are determined accurately, the gap between the average response spectrum and the design spectrum is significantly minimized. This program operates with two genetics that run concurrently, yielding results that closely approximate the optimal solution. The program itself is capable of offering users a range of desired coefficients, as well as values for the covariance and mutation of each chromosome. The algorithm detailed in this article can generate a new generation of individuals from an infinite array of ground motion records, utilizing processes such as natural selection, mating, and mutation, and continue this cycle until an individual meets the desired characteristics. This paper presents a novel method for optimally selecting accelerometers and scaling them for dynamic time history analysis, aiming for an average response spectrum that closely aligns with the target spectrum, reflecting the expected seismic activity for the structure in Tempe district in Arizona State. Given the relatively high number of parameters involved, reliance on trial-and-error methods is significantly influenced by the user’s skill set; thus, the hybrid genetic algorithm presented here addresses this limitation.

Multivariate time-series clustering of cardiopulmonary exercise test data for cardiovascular risk stratification

Abstract Aims Current clinical practice assesses cardiorespiratory fitness (CRF) by evaluating summary indexes of cardiopulmonary exercise tests (CPET). Yet, the raw time series recordings may hold additional information with clinical relevance. In this study, we investigated if the interpretation of raw CPET data could identify distinct CRF phenogroups and improve risk stratification. Methods In 1399 participants (mean age, 56.4 years; 37.7% women), who underwent maximal CPET by cycle ergometer, we collected baseline clinical characteristics and information on incident cardiovascular (CV) events (n=297) on average 4.3 years later. We employed dynamic time warping combined with k-medoids to identify phenogroups from raw CPET time-series. To evaluate the clinical significance of the derived phenogroups we compared clinical characteristics and incidence of CV events, while an external population cohort (n=171) was used to further validate the trained model. Results The optimal number of clusters was 5. We observed significant differences in age, use of medication, spirometry indexes and disease prevalence across all clusters. Cluster 5 was associated with the worst CV profile with higher use of antihypertensive medication and history of CV disease while cluster 1 represented the most favourable risk profile. After adjusting for traditional clinical covariables, clusters 4 (HR: 1.30; 95%CI: 1.02-1.65; p=0.033) and 5 (HR: 1.36; 95%CI: 1.08-1.72; p=0.0088) had significantly higher risk for incident CV events compared to clusters 1 and 2. Comparing clinical characteristics across clusters in the external validation cohort revealed similar patterns. Conclusion – Employing unsupervised machine learning on time series CPET recordings, we identified clinically meaningful CRF phenogroups. An integrative CRF profiling might facilitate CV risk stratification and consequently risk management.

Early Internal Short Circuit Diagnosis for Lithium-Ion Battery Packs Based on Dynamic Time Warping of Incremental Capacity

Timely identification of early internal short circuit faults, commonly referred to as micro short circuits (MSCs), is essential yet poses significant challenges for the safe and reliable operation of lithium-ion battery (LIB) energy storage systems. This paper introduces an innovative diagnostic method for early internal short circuits in LIB packs, utilizing dynamic time warping (DTW) applied to incremental capacity (IC). Initially, the terminal voltages of all cells within the LIB pack are ordered at any moment to determine the median terminal voltage, which is then used to generate the median IC curve. This curve acts as a reference benchmark that represents the condition of healthy cells in the pack. Subsequently, the DTW algorithm is utilized to measure the similarity between each cell’s IC curve and the median IC curve. Cells exhibiting similarity scores that exceed a specified threshold are identified as having MSC faults. Lastly, for the cells diagnosed with MSC conditions, a method for estimating short-circuit resistance (SR) based on variations in maximum charging voltage is devised to quantitatively evaluate the severity and evolution of the MSC. Experimental findings reveal that the proposed method effectively identifies MSC cells in the LIB pack and estimates their SRs without the necessity of a battery model, thereby affirming the method’s validity.