An Analysis Tool for Push-Sum Based Distributed Optimization

The push-sum algorithm is probably the most important distributed averaging approach over directed graphs, which has been applied to various problems including distributed optimization. This paper establishes the explicit absolute probability sequence for the push-sum algorithm, and based on which, constructs quadratic Lyapunov functions for push-sum based distributed optimization algorithms. As illustrative examples, the proposed novel analysis tool can improve the convergence rates of the subgradient-push and stochastic gradient-push, two important algorithms for distributed convex optimization over unbalanced directed graphs. Specifically, the paper proves that the subgradient-push algorithm converges at a rate of $O(1/\sqrt{t})$ for general convex functions and stochastic gradient-push algorithm converges at a rate of $O(1/t)$ for strongly convex functions, over time-varying unbalanced directed graphs. Both rates are respectively the same as the state-of-the-art rates of their single-agent counterparts and thus optimal, which closes the theoretical gap between the centralized and push-sum based (sub)gradient methods. The paper further proposes a heterogeneous push-sum based subgradient algorithm in which each agent can arbitrarily switch between subgradient-push and push-subgradient. The heterogeneous algorithm thus subsumes both subgradient-push and push-subgradient as special cases, and still converges to an optimal point at an optimal rate. The proposed tool can also be extended to analyze distributed weighted averaging.Comment: arXiv admin note: substantial text overlap with arXiv:2203.16623, arXiv:2303.1706

Understanding Patient Journeys with Telehealth: A Poisson-Factor-Marked Hawkes Process

The emerging telehealth platforms connect patients with physicians using telecommunication technologies and are transforming the traditional healthcare delivery process. Meanwhile, patient care journeys spreading across online and offline health service channels call for new research methodologies. Using a dataset from a telehealth platform, we develop a novel Poisson-factor-marked Hawkes process to model such a journey and quantify the mutual-modulating effects of various patient activities. Our estimation results demonstrate the disparate impacts of the patient’s health conditions and physician characteristics on choosing care channels. Taking advantage of the self-generation property of our model, we simulate policy and strategic interventions, which highlights the practical value of the proposed model and offers implications for better patient routing and service design for telehealth platforms

Study on the Formalized Development of the Street Stall Economybased on Domestic and International Experiences and Perspectives

The ground-floor economy has a long history as a significant part of the informal economy. Due to the dependence on its own social status and relationship to the government’s political and economic objectives, it has developed precariously in recent years. In the face of post-epidemic problems, a shortcut is to learn from international experience. This paper used the structural theory and drew from the secondary data, demonstrating the background of informal economy and exploring the rational ways to maintain and develop street vending. Spatialization, legalization and network digitization are proven international approaches, which display the empirical and theoretical implications to urban practice and studies

The Evolution of Measurement Methods of Comparative Advantage and New Trends in IntraProduct International Specialization

In the development and the evolution of international trade theory, comparative advantage has always been a core concept. A great deal of research pertains to the calculation methods of comparative advantage. However, most previous research on measurement methods of comparative advantage is mainly based on a country's import/export volume of a specific industry or product. Under the circumstances of contemporary intra-product international specialization, previous measurement methods are not appropriate. It is imperative to improve original measure methods of comparative advantage through stripping overseas contents of exports, and putting forward a new measurement index reflecting the domestic contents of export