Distributed two-time-scale methods over clustered networks

In this paper, we consider consensus problems over a network of nodes, where the network is divided into a number of clusters. We are interested in the case where the communication topology within each cluster is dense as compared to the sparse communication across the clusters. Moreover, each cluster has one leader which can communicate with other leaders in different clusters. The goal of the nodes is to agree at some common value under the presence of communication delays across the clusters. Our main contribution is to propose a novel distributed two-time-scale consensus algorithm, which pertains to the separation in network topology of clustered networks. In particular, one scale is to model the dynamic of the agents in each cluster, which is much faster (due to the dense communication) than the scale describing the slowly aggregated evolution between the clusters (due to the sparse communication). We prove the convergence of the proposed method in the presence of uniform, but possibly arbitrarily large, communication delays between the leaders. In addition, we provided an explicit formula for the convergence rate of such algorithm, which characterizes the impact of delays and the network topology. Our results shows that after a transient time characterized by the topology of each cluster, the convergence of the two-time-scale consensus method only depends on the connectivity of the leaders. Finally, we validate our theoretical results by a number of numerical simulations on different clustered networks

Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters

This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that, the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture. We show that this filter is an algorithm in between the Kalman filter and the particle filter, and therefore is referred to as the particle Kalman filter (PKF). In the PKF, the solution of a nonlinear filtering problem is expressed as the weighted average of an "ensemble of Kalman filters" operating in parallel. Running an ensemble of Kalman filters is, however, computationally prohibitive for realistic atmospheric and oceanic data assimilation problems. For this reason, we consider the construction of the PKF through an "ensemble" of ensemble Kalman filters (EnKFs) instead, and call the implementation the particle EnKF (PEnKF). We show that different types of the EnKFs can be considered as special cases of the PEnKF. Similar to the situation in the particle filter, we also introduce a re-sampling step to the PEnKF in order to reduce the risk of weights collapse and improve the performance of the filter. Numerical experiments with the strongly nonlinear Lorenz-96 model are presented and discussed.Comment: Accepted manuscript, to appear in Monthly Weather Revie

К проблеме методологического статуса персонализированной медицины как практикоориентарованной учебной дисциплины

МЕДИЦИНСКИЕ УЧЕБНЫЕ ЗАВЕДЕНИЯОБРАЗОВАНИЕ МЕДИЦИНСКОЕСТУДЕНТЫУЧЕБНЫЕ ДИСЦИПЛИНЫПЕРСОНАЛИЗИРОВАННАЯ МЕДИЦИНАПРАКТИКО-ОРИЕНТИРОВАННАЯ ОБРАЗОВАТЕЛЬНАЯ СРЕДАПРАКТИКО-ОРИЕНТИРОВАННОЕ ОБУЧЕНИЕМЕТОДОЛОГИЧЕСКИЕ ПОДХОД

Unveiling the role of artificial intelligence for wound assessment and wound healing prediction

Wound healing is a very dynamic and complex process as it involves the patient, wound-level parameters, as well as biological, environmental, and socioeconomic factors. Its process includes hemostasis, inflammation, proliferation, and remodeling. Evaluation of wound components such as angiogenesis, inflammation, restoration of connective tissue matrix, wound contraction, remodeling, and re-epithelization would detail the healing process. Understanding key mechanisms in the healing process is critical to wound research. Elucidating its healing complexity would enable control and optimize the processes for achieving faster healing, preventing wound complications, and undesired outcomes such as infection, periwound dermatitis and edema, hematomas, dehiscence, maceration, or scarring. Wound assessment is an essential step for selecting an appropriate treatment and evaluating the wound healing process. The use of artificial intelligence (AI) as advanced computer-assisted methods is promising for gaining insights into wound assessment and healing. As AI-based approaches have been explored for various applications in wound care and research, this paper provides an overview of recent studies exploring the application of AI and its technical developments and suitability for accurate wound assessment and prediction of wound healing. Several studies have been done across the globe, especially in North America, Europe, Oceania, and Asia. The results of these studies have shown that AI-based approaches are promising for wound assessment and prediction of wound healing. However, there are still some limitations and challenges that need to be addressed. This paper also discusses the challenges and limitations of AI-based approaches for wound assessment and prediction of wound healing. The paper concludes with a discussion of future research directions and recommendations for the use of AI-based approaches for wound assessment and prediction of wound healing