Harmonic-Copuled Riccati Equations and its Applications in Distributed Filtering

The coupled Riccati equations are cosisted of multiple Riccati-like equations with solutions coupled with each other, which can be applied to depict the properties of more complex systems such as markovian systems or multi-agent systems. This paper manages to formulate and investigate a new kind of coupled Riccati equations, called harmonic-coupled Riccati equations (HCRE), from the matrix iterative law of the consensus on information-based distributed filtering (CIDF) algortihm proposed in [1], where the solutions of the equations are coupled with harmonic means. Firstly, mild conditions of the existence and uniqueness of the solution to HCRE are induced with collective observability and primitiviness of weighting matrix. Then, it is proved that the matrix iterative law of CIDF will converge to the unique solution of the corresponding HCRE, hence can be used to obtain the solution to HCRE. Moreover, through applying the novel theory of HCRE, it is pointed out that the real estimation error covariance of CIDF will also become steady-state and the convergent value is simplified as the solution to a discrete time Lyapunov equation (DLE). Altogether, these new results develop the theory of the coupled Riccati equations, and provide a novel perspective on the performance analysis of CIDF algorithm, which sufficiently reduces the conservativeness of the evaluation techniques in the literature. Finally, the theoretical results are verified with numerical experiments.Comment: 14 pages, 4 figure

A Bayesian Circadian Hidden Markov Model to Infer Rest-Activity Rhythms Using 24-hour Actigraphy Data

24-hour actigraphy data collected by wearable devices offer valuable insights into physical activity types, intensity levels, and rest-activity rhythms (RAR). RARs, or patterns of rest and activity exhibited over a 24-hour period, are regulated by the body's circadian system, synchronizing physiological processes with external cues like the light-dark cycle. Disruptions to these rhythms, such as irregular sleep patterns, daytime drowsiness or shift work, have been linked to adverse health outcomes including metabolic disorders, cardiovascular disease, depression, and even cancer, making RARs a critical area of health research. In this study, we propose a Bayesian Circadian Hidden Markov Model (BCHMM) that explicitly incorporates 24-hour circadian oscillators mirroring human biological rhythms. The model assumes that observed activity counts are conditional on hidden activity states through Gaussian emission densities, with transition probabilities modeled by state-specific sinusoidal functions. Our comprehensive simulation study reveals that BCHMM outperforms frequentist approaches in identifying the underlying hidden states, particularly when the activity states are difficult to separate. BCHMM also excels with smaller Kullback-Leibler divergence on estimated densities. With the Bayesian framework, we address the label-switching problem inherent to hidden Markov models via a positive constraint on mean parameters. From the proposed BCHMM, we can infer the 24-hour rest-activity profile via time-varying state probabilities, to characterize the person-level RAR. We demonstrate the utility of the proposed BCHMM using 2011-2014 National Health and Nutrition Examination Survey (NHANES) data, where worsened RAR, indicated by lower probabilities in low-activity state during the day and higher probabilities in high-activity state at night, is associated with an increased risk of diabetes

Consensus-Based Distributed Filtering with Fusion Step Analysis

For consensus on measurement-based distributed filtering (CMDF), through infinite consensus fusion operations during each sampling interval, each node in the sensor network can achieve optimal filtering performance with centralized filtering. However, due to the limited communication resources in physical systems, the number of fusion steps cannot be infinite. To deal with this issue, the present paper analyzes the performance of CMDF with finite consensus fusion operations. First, by introducing a modified discrete-time algebraic Riccati equation and several novel techniques, the convergence of the estimation error covariance matrix of each sensor is guaranteed under a collective observability condition. In particular, the steady-state covariance matrix can be simplified as the solution to a discrete-time Lyapunov equation. Moreover, the performance degradation induced by reduced fusion frequency is obtained in closed form, which establishes an analytical relation between the performance of the CMDF with finite fusion steps and that of centralized filtering. Meanwhile, it provides a trade-off between the filtering performance and the communication cost. Furthermore, it is shown that the steady-state estimation error covariance matrix exponentially converges to the centralized optimal steady-state matrix with fusion operations tending to infinity during each sampling interval. Finally, the theoretical results are verified with illustrative numerical experiments

HyPar: Towards Hybrid Parallelism for Deep Learning Accelerator Array

With the rise of artificial intelligence in recent years, Deep Neural Networks (DNNs) have been widely used in many domains. To achieve high performance and energy efficiency, hardware acceleration (especially inference) of DNNs is intensively studied both in academia and industry. However, we still face two challenges: large DNN models and datasets, which incur frequent off-chip memory accesses; and the training of DNNs, which is not well-explored in recent accelerator designs. To truly provide high throughput and energy efficient acceleration for the training of deep and large models, we inevitably need to use multiple accelerators to explore the coarse-grain parallelism, compared to the fine-grain parallelism inside a layer considered in most of the existing architectures. It poses the key research question to seek the best organization of computation and dataflow among accelerators. In this paper, we propose a solution HyPar to determine layer-wise parallelism for deep neural network training with an array of DNN accelerators. HyPar partitions the feature map tensors (input and output), the kernel tensors, the gradient tensors, and the error tensors for the DNN accelerators. A partition constitutes the choice of parallelism for weighted layers. The optimization target is to search a partition that minimizes the total communication during training a complete DNN. To solve this problem, we propose a communication model to explain the source and amount of communications. Then, we use a hierarchical layer-wise dynamic programming method to search for the partition for each layer.Comment: To appear in the 2019 25th International Symposium on High-Performance Computer Architecture (HPCA 2019

Us adolescent Rest-Activity Patterns: insights From Functional Principal Component analysis (Nhanes 2011-2014)

BACKGROUND: Suboptimal rest-activity patterns in adolescence are associated with worse health outcomes in adulthood. Understanding sociodemographic factors associated with rest-activity rhythms may help identify subgroups who may benefit from interventions. This study aimed to investigate the association of rest-activity rhythm with demographic and socioeconomic characteristics in adolescents. METHODS: Using cross-sectional data from the nationally representative National Health and Nutrition Examination Survey (NHANES) 2011-2014 adolescents (N = 1814), this study derived rest-activity profiles from 7-day 24-hour accelerometer data using functional principal component analysis. Multiple linear regression was used to assess the association between participant characteristics and rest-activity profiles. Weekday and weekend specific analyses were performed in addition to the overall analysis. RESULTS: Four rest-activity rhythm profiles were identified, which explained a total of 82.7% of variance in the study sample, including (1) High amplitude profile; (2) Early activity window profile; (3) Early activity peak profile; and (4) Prolonged activity/reduced rest window profile. The rest-activity profiles were associated with subgroups of age, sex, race/ethnicity, and household income. On average, older age was associated with a lower value for the high amplitude and early activity window profiles, but a higher value for the early activity peak and prolonged activity/reduced rest window profiles. Compared to boys, girls had a higher value for the prolonged activity/reduced rest window profiles. When compared to Non-Hispanic White adolescents, Asian showed a lower value for the high amplitude profile, Mexican American group showed a higher value for the early activity window profile, and the Non-Hispanic Black group showed a higher value for the prolonged activity/reduced rest window profiles. Adolescents reported the lowest household income had the lowest average value for the early activity window profile. CONCLUSIONS: This study characterized main rest-activity profiles among the US adolescents, and demonstrated that demographic and socioeconomic status factors may shape rest-activity behaviors in this population

Artificial Light at Night and Social Vulnerability: an Environmental Justice analysis in the US 2012-2019

BACKGROUND: Artificial Light at Night (ALAN) is an emerging health risk factor that has been linked to a wide range of adverse health effects. Recent study suggested that disadvantaged neighborhoods may be exposed to higher levels of ALAN. Understanding how social disadvantage correlates with ALAN levels is essential for identifying the vulnerable populations and for informing lighting policy. METHODS: We used satellite data from the National Aeronautics and Space Administration\u27s (NASA) Black Marble data product to quantify annual ALAN levels (2012-2019), and the Center for Disease Control and Prevention\u27s (CDC) Social Vulnerability Index (SVI) to quantify social disadvantage, both at the US census tract level. We examined the relationship between the ALAN and SVI (overall and domain-specific) in over 70,000 tracts in the Contiguous U.S., and investigated the heterogeneities in this relationship by the rural-urban status and US regions (i.e., Northeast, Midwest, South, West). RESULTS: We found a significant positive relationship between SVI and ALAN levels. On average, the ALAN level in the top 20% most vulnerable communities was 2.46-fold higher than that in the 20% least vulnerable communities (beta coefficient (95% confidence interval) for log-transformed ALAN, 0.90 (0.88, 0.92)). Of the four SVI domains, minority and language status emerged as strong predictors of ALAN levels. Our stratified analysis showed considerable and complex heterogeneities across different rural-urban categories, with the association between greater vulnerability and higher ALAN primarily observed in urban cores and rural areas. We also found regional differences in the association between ALAN and both overall SVI and SVI domains. CONCLUSIONS: Our study suggested ALAN as an environmental justice issue that may carry important public health implications. Funding National Aeronautics and Space Administration

Infrared Imaging of Magnetic Octupole Domains in Non-collinear Antiferromagnets

Magnetic structure plays a pivotal role in the functionality of antiferromagnets (AFMs), which not only can be employed to encode digital data but also yields novel phenomena. Despite its growing significance, visualizing the antiferromagnetic domain structure remains a challenge, particularly for non-collinear AFMs. Currently, the observation of magnetic domains in non-collinear antiferromagnetic materials is feasible only in Mn$_{3}$Sn, underscoring the limitations of existing techniques that necessitate distinct methods for in-plane and out-of-plane magnetic domain imaging. In this study, we present a versatile method for imaging the antiferromagnetic domain structure in a series of non-collinear antiferromagnetic materials by utilizing the anomalous Ettingshausen effect (AEE), which resolves both the magnetic octupole moments parallel and perpendicular to the sample surface. Temperature modulation due to the AEE originating from different magnetic domains is measured by the lock-in thermography, revealing distinct behaviors of octupole domains in different antiferromagnets. This work delivers an efficient technique for the visualization of magnetic domains in non-collinear AFMs, which enables comprehensive study of the magnetization process at the microscopic level and paves the way for potential advancements in applications.Comment: National Science Review in pres