Temporal Regularity Research Articles

Regularity theory for a new class of fractional parabolic stochastic evolution equations

A new class of fractional-order parabolic stochastic evolution equations of the form (∂t+A)γX(t)=W˙Q(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\partial _t + A)^\\gamma X(t) = {\\dot{W}}^Q(t)$$\\end{document}, t∈[0,T]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t\\in [0,T]$$\\end{document}, γ∈(0,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma \\in (0,\\infty )$$\\end{document}, is introduced, where -A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-A$$\\end{document} generates a C0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_0$$\\end{document}-semigroup on a separable Hilbert space H and the spatiotemporal driving noise W˙Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\dot{W}}^Q$$\\end{document} is the formal time derivative of an H-valued cylindrical Q-Wiener process. Mild and weak solutions are defined; these concepts are shown to be equivalent and to lead to well-posed problems. Temporal and spatial regularity of the solution process X are investigated, the former being measured by mean-square or pathwise smoothness and the latter by using domains of fractional powers of A. In addition, the covariance of X and its long-time behavior are analyzed. These abstract results are applied to the cases when A:=Lβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A:= L^\\beta $$\\end{document} and Q:=L~-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q:={\\widetilde{L}}^{-\\alpha }$$\\end{document} are fractional powers of symmetric, strongly elliptic second-order differential operators defined on (i) bounded Euclidean domains or (ii) smooth, compact surfaces. In these cases, the Gaussian solution processes can be seen as generalizations of merely spatial (Whittle–)Matérn fields to space–time.

Predictions and rewards affect decision-making but not subjective experience.

To survive, organisms constantly make decisions to avoid danger and maximize rewards in information-rich environments. As a result, decisions about sensory input are not only driven by sensory information but also by other factors, such as the expected rewards of a decision (known as the payoff matrix) or by information about temporal regularities in the environment (known as cognitive priors or predictions). However, it is unknown to what extent these different types of information affect subjective experience or whether they merely result in nonperceptual response criterion shifts. To investigate this question, we used three carefully matched manipulations that typically result in behavioral shifts in decision criteria: a visual illusion (Müller-Lyer condition), a punishment scheme (payoff condition), and a change in the ratio of relevant stimuli (base rate condition). To gauge shifts in subjective experience, we introduce a task in which participants not only make decisions about what they have just seen but are also asked to reproduce their experience of a target stimulus. Using Bayesian ordinal modeling, we show that each of these three manipulations affects the decision criterion as intended but that the visual illusion uniquely affects sensory experience as measured by reproduction. In a series of follow-up experiments, we use computational modeling to show that although the visual illusion results in a distinct drift-diffusion (DDM) parameter profile relative to nonsensory manipulations, reliance on DDM parameter estimates alone is not sufficient to ascertain whether a given manipulation is perceptual or nonperceptual.

Temporal regularity in autobiographical memory: A single case fMRI study.

Using fMRI, precise temporal control was extracted from routine activities in a female blind subject. Findings reveal a specific neural machinery for temporal control of recalled sequential events in episodic memory.

Exploring incomplete decoupling modeling with window and cross-window mechanism for skeleton-based action recognition

Skeleton-based action recognition relies on capturing connections between joints to extract action-specific features. Current approaches utilizing temporal convolution for inter-frame joint relationships only capture connections within the same joint across different frames. It neglects potential connections between joints in different frames. However, modeling all joints across frames will encode a plethora of redundant features that impede the recognition of action. In this study, a novel and effective skeleton window attention mechanism (SWAM) is proposed that consists of window attention module (WAM) and spatial–temporal attention regularization (STAR). WAM directly capture short-range features within isolated windows. It consolidates all joints from adjacent frames into the window and performs full attention operations on them. STAR enhances the model’s focus on structural action features, counteracting the vanilla attention mechanism’s oversight. Furthermore, this study introduces the cross-window mechanism (CWM) that consists of three components: cross-window fusion (CWF), cross-window shift (CWS), and cross-window aggregation (CWA). These components collectively break the limitations imposed by window boundaries, enabling efficient interactions between windows and facilitating the capture of long-range dependencies. Integrating SWAM and CWM, we introduce the skeleton window attention network (SWA-Net), which embodies a novel approach of incomplete decoupling modeling. It can extract action features from different joints in different frames without capturing excessive redundant features. Compared with the state-of-the-art methods, it achieves better results on NTU-RGB+D, NTU-RGB+D 120 and Kinetics-Skeleton 400 datasets.

Macaque monkeys and humans sample temporal regularities in the acoustic environment.

Many animal species show comparable abilities to detect basic rhythms and produce rhythmic behavior. Yet, the capacities to process complex rhythms and synchronize rhythmic behavior appear to be species-specific: vocal learning animals can, but some primates might not. This discrepancy is of high interest as there is a putative link between rhythm processing and the development of sophisticated sensorimotor behavior in humans. Do our closest ancestors show comparable endogenous dispositions to sample the acoustic environment in the absence of task instructions and training? We recorded EEG from macaque monkeys and humans while they passively listened to isochronous equitone sequences. Individual- and trial-level analyses showed that macaque monkeys' and humans' delta-band neural oscillations encoded and tracked the timing of auditory events. Further, mu- (8-15Hz) and beta-band (12-20Hz) oscillations revealed the superimposition of varied accentuation patterns on a subset of trials. These observations suggest convergence in the encoding and dynamic attending of temporal regularities in the acoustic environment, bridging a gap in the phylogenesis of rhythm cognition.

Vehicle Trajectory Completion for Automatic Number Plate Recognition Data: A Temporal Knowledge Graph-Based Method

Vehicle trajectories represent an essential information source in intelligent transportation systems. Prior trajectory completion models based on Automatic Number Plate Recognition (ANPR) data have typically depended on vehicle re-identification results or road network information or have employed static knowledge graphs to integrate the two information sources. However, these methods have not taken into account the implicit temporal characteristics of trajectories in ANPR data and have neglected individual vehicle preferences. To address this void, this study proposes a Temporal Knowledge Graph-based Vehicle Trajectory Completion Model (TKG-VTC). The model implementation comprises three stages: first, ANPR data are converted into a temporal trajectory knowledge graph; second, knowledge representation learning is conducted using nontemporal relations, a biased temporal regularizer and multivector embeddings to embed the knowledge on the graph; and finally, the embedded results are employed to perform link prediction for incomplete trajectories, thereby restoring vehicle trajectories in ANPR data. Through model evaluation metrics and dimensionality reduction experiments, TKG-VTC is observed to demonstrate the best performance in completing trajectories when compared to TComplEx, TNTComplEx, and TeLM. This research introduces an innovative application of employing temporal knowledge graphs for trajectory reconstruction, which eliminates dependence on vehicle re-identification and road network information in previous methodologies. This is advantageous for enhancing the performance and dependability of vehicle trajectory data in intelligent transportation systems, as well as facilitating the implementation of trajectory prediction, demand analysis, and accident warning applications.

Effects of age-related cochlear deafferentation and central gain on auditory scene analysis

Animal models show that cochlear afferent nerve endings are more vulnerable than sensory hair cells to age-related damage. Because such cochlear deafferentation is not apparent in standard audiometry, the extent to which it contributes to deficits in human hearing is debated, and the intervening neural processes are poorly characterized. This presentation will describe our efforts to address these gaps through co-ordinated experiments in at-risk humans and a chinchilla model. Our results suggest that cochlear deafferentation is widespread in middle age despite clinically normal audiometric sensitivity. Furthermore, the resulting reduction in peripheral input appears to trigger compensatory central “gain” at the cortical level, likely through altered local balance of excitation and inhibition. Consistent with the important role of inhibition in parsing temporal regularities across different frequency components of sound, central gain is also associated with reduced ability to perceptually segregate acoustic scenes with multiple sources into individual perceptual streams. Taken together, our results suggest that age-related cochlear deafferentation may affect hearing not only by reducing the fidelity of input encoding but also by interfering with the central auditory system’s ability to extract targets in noisy environments.

Temporal segment dropout for human action video recognition

Temporal information is important for human action video recognition. With the widely used spatio-temporal neural networks, researchers have found that the learned high-level features preserve overfitted spatial information and limited temporal information, leading to inferior performance. This is because existing networks lack efficient regularization for the temporal structure. To learn more robust temporal features, we propose a temporal regularization method named Temporal Segment Dropout (TSD). TSD drops the most salient spatial features in order to enhance the temporal features in a clip of temporal segments. Without learning from complex examples, TSD can be easily deployed in existing networks. In the experiment, TSD is extensively evaluated on benchmark action recognition datasets, which brings consistent improvements over the baselines, especially for the action-centric classes.

Output Feedback Stabilization of Doubly Fed Induction Generator Wind Turbines under Event-Triggered Implementations

The robust stabilization of doubly fed induction generators in wind turbines against external disturbances is considered in this study. It is assumed that the angular speeds of wind turbines can only be measured and sent to the controller in a discrete-time fashion over a network. To generate the sampling times, three different triggering schemes were developed: time-triggering, static event-triggering, and dynamic event-triggering mechanisms; moreover, performance comparisons were conducted between such approaches. The design methodology is based on emulation, such that the plant is first stabilized in continuous-time where a robust feedback law is constructed based on the linear quadratic Gaussian regulator (LQG) approach. Then, the impact of the network is taken into account, and an event-triggering mechanism is built so that closed-loop stability is maintained and the Zeno phenomenon is avoided by using temporal regularization. The necessary stability constraints are framed as a linear matrix inequality, and the whole system is modeled as a hybrid dynamical system. A numerical simulation is used to demonstrate the effectiveness of the control strategy. The results show that the event-triggering mechanisms achieve a significant reduction of around 50% in transmissions compared to periodic sampling. Moreover, numerical comparisons with existing approaches show that the proposed approach provides better performance in terms of the stability guarantee and number of transmissions.

A combined method of autoregressive model and matrix factorization for recovery and forecasting of cyclic structural health monitoring data

Structures such as bridges, offshore platforms, wind power facilities, and drilling rigs generate a corresponding periodic structural response under cyclic loads such as solar radiation, tides and sea-land breeze. Data recovery and forecasting are major parts of the work to ensure structural safety using periodic structural health monitoring data. In this context, a combined method of autoregressive (AR) model and matrix factorization (MF) method is presented to reaching the tasks of data imputation and prediction. The combined method with a graph-based temporal regularizer can well capture the cyclic characteristics and random character. The verification of the method is conducted using an in-situ temperature monitoring dataset of a high-speed railway steel bridge. The application of the method for both data recovery and forecasting with structured missing entries is carried out, which indicates the combined method owns outstanding performance in accurately recover missing entries and making predictions. In the last part, the analysis of rank order and length of time lag is made to show its influence on imputation accuracy.

Learning dynamic spatial-temporal regularized correlation filter tracking with response deviation suppression via multi-feature fusion

Visual object tracking (VOT) for intelligent video surveillance has attracted great attention in the current research community, thanks to advances in computer vision and camera technology. Meanwhile, discriminative correlation filter (DCF) trackers garnered significant interest owing to their high accuracy and low computing cost. Many researchers have introduced spatial and temporal regularization into the DCF framework to achieve a more robust appearance model and further improve tracking performance. However, these algorithms typically set fixed spatial and temporal regularization parameters, which limit flexibility and adaptability under cluttered and challenging scenarios. To overcome these problems, in this work, we propose a new dynamic spatial–temporal regularization for the DCF tracking model that emphasizes the filter to concentrate on more reliable regions during the training stage. Furthermore, we present a response deviation-suppressed regularization term for responses to encourage temporal consistency and avoid model degradation by suppressing relative response changes between two consecutive frames. Moreover, we introduce a multi-memory tracking framework to exploit various features and each memory contributes to tracking the target across all frames. Significant experiments on the OTB-2013, OTB-2015, TC-128, UAV-123, UAVDT, and DTB-70 datasets have revealed that the performance thereof outperformed many state-of-the-art trackers based on DCF and deep-based frameworks in terms of tracking accuracy and tracking success rate.

On Temporal Regularity of Strong Solutions to Stochastic \(p\)-Laplace Systems

On Temporal Regularity of Strong Solutions to Stochastic \(p\)-Laplace Systems

Data-driven identification of household-transformer relationships in power distribution networks using Hausdorff similarity assessment

Precisely identifying the household-transformer relationship is of significant importance for both the stability of the power system and the quality of customer electricity consumption. However, the complex network structures and frequent reconfigurations may lead to inaccurate records of household-transformer relationships. In this paper, a novel data-driven similarity assessment solution is proposed to enhance the accuracy and scalability of identifying household-transformer relationships. Initially, a data processing method based on dynamic temporal regularization with sliding windows is employed to optimize dataset quality as well as enhance the efficiency of data processing. Then, a two-stage solution is proposed for identifying the household-transformer relationship. The first stage involves initial normalized clustering based on the basic information of power distribution substations, while the second stage assesses the similarity between households and transformer operational states based on Hausdorff distance. The superior performance of the proposed method is extensively assessed through real historical datasets, compared to benchmarks.

Flexible structure learning under uncertainty.

Experience is known to facilitate our ability to interpret sequences of events and make predictions about the future by extracting temporal regularities in our environments. Here, we ask whether uncertainty in dynamic environments affects our ability to learn predictive structures. We exposed participants to sequences of symbols determined by first-order Markov models and asked them to indicate which symbol they expected to follow each sequence. We introduced uncertainty in this prediction task by manipulating the: (a) probability of symbol co-occurrence, (b) stimulus presentation rate. Further, we manipulated feedback, as it is known to play a key role in resolving uncertainty. Our results demonstrate that increasing the similarity in the probabilities of symbol co-occurrence impaired performance on the prediction task. In contrast, increasing uncertainty in stimulus presentation rate by introducing temporal jitter resulted in participants adopting a strategy closer to probability maximization than matching and improving in the prediction tasks. Next, we show that feedback plays a key role in learning predictive statistics. Trial-by-trial feedback yielded stronger improvement than block feedback or no feedback; that is, participants adopted a strategy closer to probability maximization and showed stronger improvement when trained with trial-by-trial feedback. Further, correlating individual strategy with learning performance showed better performance in structure learning for observers who adopted a strategy closer to maximization. Our results indicate that executive cognitive functions (i.e., selective attention) may account for this individual variability in strategy and structure learning ability. Taken together, our results provide evidence for flexible structure learning; individuals adapt their decision strategy closer to probability maximization, reducing uncertainty in temporal sequences and improving their ability to learn predictive statistics in variable environments.

Temporal imprecision and phase instability in schizophrenia resting state EEG

Schizophrenia is characterized by temporal imprecision and irregularities on neuronal, psychological cognitive, and behavioral levels which are usually tested during task-related activity. This leaves open whether analogous temporal imprecision and irregularities can already be observed in the brain's spontaneous activity as measured during the resting state; this is the goal of our study. Building on recent task-related data, we, using EEG, aimed to investigate the temporal precision and regularity of phase coherence over time in healthy, schizophrenia, and bipolar disorder participants. To this end, we developed a novel methodology, nominal frequency phase stability (NFPS), that allows to measure stability over phase angles in selected frequencies. By applying sample entropy quantification to the time-series of the nominal frequency phase angle time series, we found increased irregularities in theta activity over a frontocentral electrode in schizophrenia but not in bipolar disorder. We therefore assume that temporal imprecision and irregularity already occur in the brain's spontaneous activity in schizophrenia.

Polar ionospheric currents and high temporal resolution geomagnetic field models

SUMMARY Estimating high resolution models of the Earth’s core magnetic field and its time variation in the polar regions requires that one can adequately account for magnetic signals produced by polar ionospheric currents, which vary on a wide range of time and length scales. Limitations of existing ionospheric field models in the challenging polar regions can adversely affect core field models, which in turn has important implications for studies of the core flow dynamics in those regions. Here we implement a new approach to co-estimate a climatological model of the ionospheric field together with a model of the internal and magnetospheric fields within the CHAOS geomagnetic field modelling framework. The parametrization of the ionospheric field exploits non-orthogonal magnetic coordinates to efficiently account for the geometry of the Earth’s magnetic field and scales linearly with external driving parameters related to the solar wind and the interplanetary magnetic field. Using this approach we derive a new geomagnetic field model from measurements of the magnetic field collected by low Earth orbit satellites, which in addition to the internal field provides estimates of the typical current system in the polar ionosphere and successfully accounts for previously unmodelled ionospheric signals in field model residuals. To resolve the ambiguity between the internal and ionospheric fields when using satellite data alone, we impose regularization. We find that the time derivative of the estimated internal field is less contaminated by the polar currents, which is mostly visible in the zonal and near-zonal terms at high spherical harmonic degrees. Distinctive patches of strong secular variation at the core–mantle boundary, which have important implications for core dynamics, persist. Relaxing the temporal regularization reveals annual oscillations, which could indicate remaining ionospheric field or related induced signals in the internal field model. Using principal component analysis we find that the annual oscillations mostly affect the zonal low-degree spherical harmonics of the internal field.

Speech Enhancement Based on Constrained Low-rank Sparse Matrix Decomposition Integrated with Temporal Continuity Regularisation

Speech enhancement in strong noise condition is a challenging problem. Low-rank and sparse matrix decomposition (LSMD) theory has been applied to speech enhancement recently and good performance was obtained. Existing LSMD algorithms consider each frame as an individual observation. However, real-world speeches usually have a temporal structure, and their acoustic characteristics vary slowly as a function of time. In this paper, we propose a temporal continuity constrained low-rank sparse matrix decomposition (TCCLSMD) based speech enhancement method. In this method, speech separation is formulated as a TCCLSMD problem and temporal continuity constraints are imposed in the LSMD process. We develop an alternative optimisation algorithm for noisy spectrogram decomposition. By means of TCCLSMD, the recovery speech spectrogram is more consistent with the structure of the clean speech spectrogram, and it can lead to more stable and reasonable results than the existing LSMD algorithm. Experiments with various types of noises show the proposed algorithm can achieve a better performance than traditional speech enhancement algorithms, in terms of yielding less residual noise and lower speech distortion.

Greater temporal regularity of primary care visits was associated with reduced hospitalizations and mortality, even after controlling for continuity of care

BackgroundPrevious studies have shown that more temporally regular primary care visits are associated with improved patient outcomes.ObjectiveTo examine the association of temporal regularity (TR) of primary care with hospitalizations and mortality in patients with chronic illnesses. Also, to identify threshold values for TR for predicting outcomes.DesignRetrospective cohort study.ParticipantsWe used data from the electronic health record of a health maintenance organization in Israel to study primary care visits of 70,095 patients age 40 + with one of three chronic conditions (diabetes mellitus, heart failure, chronic obstructive pulmonary disease).Main measuresWe calculated TR for each patient during a two-year period (2016–2017), and divided patients into quintiles based on TR. Outcomes (hospitalization, death) were observed in 2018–2019. Covariates included the Bice-Boxerman continuity of care score, demographics, and comorbidities. We used multivariable logistic regression to examine TR’s association with hospitalization and death, controlling for covariates.Key resultsCompared to patients receiving the most regular care, patients receiving less regular care had increased odds of hospitalization and mortality, with a dose–response curve observed across quintiles (p for linear trend < 0.001). For example, patients with the least regular care had an adjusted odds ratio of 1.40 for all-cause mortality, compared to patients with the most regular care. Analyses stratified by age, sex, ethnic group, area-level SES, and certain comorbid conditions did not show strong differential associations of TR across groups.ConclusionsWe found an association between more temporally regular care in antecedent years and reduced hospitalization and mortality of patients with chronic illness in subsequent years, after controlling for covariates. There was no clear threshold value for temporal regularity; rather, more regular primary care appeared to be better across the entire range of the variable.

Harmonic-aware tri-path convolution recurrent network for singing voice separation

Temporal coherence and spectral regularity are critical cues for human auditory streaming processes and are considered in many sound separation models. Some examples include the Conv-tasnet model, which focuses on temporal coherence using short length kernels to analyze sound, and the dual-path convolution recurrent network (DPCRN) model, which uses two recurring neural networks to analyze general patterns along the temporal and spectral dimensions on a spectrogram. By expanding DPCRN, a harmonic-aware tri-path convolution recurrent network model via the addition of an inter-band RNN is proposed. Evaluation results on public datasets show that this addition can further boost the separation performances of DPCRN.

A Federated Learning System for Histopathology Image Analysis with an Orchestral Stain-Normalization GAN.

Currently, data-driven based machine learning is considered one of the best choices in clinical pathology analysis, and its success is subject to the sufficiency of digitized slides, particularly those with deep annotations. Although centralized training on a large data set may be more reliable and more generalized, the slides to the examination are more often than not collected from many distributed medical institutes. This brings its own challenges, and the most important is the assurance of privacy and security of incoming data samples. In the discipline of histopathology image, the universal stain-variation issue adds to the difficulty of an automatic system as different clinical institutions provide distinct stain styles. To address these two important challenges in AI-based histopathology diagnoses, this work proposes a novel conditional Generative Adversarial Network (GAN) with one orchestration generator and multiple distributed discriminators, to cope with multiple-client based stain-style normalization. Implemented within a Federated Learning (FL) paradigm, this framework well preserves data privacy and security. Additionally, the training consistency and stability of the distributed system are further enhanced by a novel temporal self-distillation regularization scheme. Empirically, on large cohorts of histopathology datasets as a benchmark, the proposed model matches the performance of conventional centralized learning very closely. It also outperforms state-of-the-art stain-style transfer methods on the downstream Federated Learning image classification task, with an accuracy increase of over 20.0% in comparison to the baseline classification model.