A model for analyzing competitive dynamics on triplex networks.

This paper studies the evolution process of competitive dynamics on triplex complex networks. We propose a new triplex network model in which the state of the node in each layer is affected by its neighbors as well as inter-layer competition. Through this model, we combine the opinion diffusion model, the Ising model, and the signed network and extend their application from single-layer to multi-layer networks. We derive the evolution process and dynamical equations of the model and carry out a series of numerical simulations to discuss the influence of several factors on the evolution process and the competitiveness of the network. First, we find that the increase of global transition threshold p or the proportion of initial active nodes will lead to more surviving layers and more active nodes in each layer. In addition, we summarize the similarities and differences of the evolution curves under different conditions. Second, we discuss the influence of initial active nodes and the average degree on the competitiveness of the network and find the correlations between them. Finally, we study the relationship between network topology and network competitiveness and conclude the conditions for the best competitiveness of the network. Based on the simulation results, we give specific suggestions on how to improve the competitiveness of the platform in reality.

Cluster synchronization: From single-layer to multi-layer networks.

Cluster synchronization is a very common phenomenon occurring in single-layer complex networks, and it can also be observed in many multilayer networks in real life. In this paper, we study cluster synchronization of an isolated network and then focus on that of the network when it is influenced by an external network. We mainly explore how the influence layer impacts the cluster synchronization of the interest layer in a multilayer network. Considering that the clusters are changeable, we introduce a term called "cluster synchronizability" to measure the ability of a network to reach cluster synchronization. Since cluster synchronizability is intimately associated with the structure of the coupled external layer, we consider community networks and networks with different densities as the coupled layer. Besides the topology structure, the connection between two layers may also have an influence on the cluster synchronization of the interest layer. We study three different patterns of connection, including typical positive correlation, negative correlation, and random correlation and find that they all have a certain influence. However, the general theoretical analysis of cluster synchronization on multilayer networks is still a challenging topic. In this paper, we mainly use numerical simulations to discuss cluster synchronization.

Regio- and Stereoselective Hydrochlorination/Cyclization of 1,n-Enynes by FeCl3 Catalysis.

A highly regio- and stereoselective hydrochlorination/cyclization of enynes has been reported by FeCl3 catalysis. A variety of enynes undergo this cyclization transformation with acetic chloride as the chlorine source and H2O providing protons via a cationic pathway. This protocol provides a cheap, simple, stereospecific, and effective cyclization to afford heterocyclic alkenyl chloride compounds as Z isomers with high yields (≤98%) and regioselectivity.

Longitudinal and time-to-event modeling for prognostic implications of radical surgery in retroperitoneal sarcoma.

Retroperitoneal sarcoma (RPS) is a rare malignancy which can be difficult to manage due to the variety of clinical behaviors. In this study, we aimed to develop a parametric modeling framework to quantify the relationship between postoperative dynamics of several biomarkers and overall/progression-free survival of RPS. One hundred seventy-four patients with RPS who received surgical resection with curative intent at the Peking University Cancer Hospital Sarcoma Center were retrospectively included. Potential prognostic factors were preliminarily identified. Longitudinal analyses of body mass index (BMI), serum total protein (TP), and white blood cells (WBCs) were performed using nonlinear mixed effects models. The impacts of time-varying and time-invariant predictors on survival were investigated by parametric time-to-event (TTE) models. The majority of patients experienced decline in BMI, recovery of TP, as well as transient elevation in WBC counts after surgery, which significantly correlated with survival. An indirect-response model incorporating surgery effect described the fluctuation in percentage BMI. The recovery of TP was captured by a modified Gompertz model, and a semimechanistic model was selected for WBCs. TTE models estimated that the daily cumulative average of predicted BMI and WBC, the seventh-day TP, as well as certain baseline variables, were significant predictors of survival. Model-based simulations were performed to examine the clinical significance of prognostic factors. The current work quantified the individual trajectories of prognostic biomarkers in response to surgery and predicted clinical outcomes, which would constitute an additional strategy for disease monitoring and intervention in postoperative RPS.