No abstract

MotivationThe evolution of complex diseases can be modeled as a time-dependent nonlinear dynamic system, and its progression can be divided into three states, i.e., the normal state, the pre-disease state and the disease state. The sudden deterioration of the disease can be regarded as the state transition of the dynamic system at the critical state or pre-disease state. How to detect the critical state of an individual before the disease state based on single-sample data has attracted many researchers’ attention.MethodsIn this study, we proposed a novel approach, i.e., single-sample-based Jensen-Shannon Divergence (sJSD) method to detect the early-warning signals of complex diseases before critical transitions based on individual single-sample data. The method aims to construct score index based on sJSD, namely, inconsistency index (ICI).ResultsThis method is applied to five real datasets, including prostate cancer, bladder urothelial carcinoma, influenza virus infection, cervical squamous cell carcinoma and endocervical adenocarcinoma and pancreatic adenocarcinoma. The critical states of 5 datasets with their corresponding sJSD signal biomarkers are successfully identified to diagnose and predict each individual sample, and some “dark genes” that without differential expressions but are sensitive to ICI score were revealed. This method is a data-driven and model-free method, which can be applied to not only disease prediction on individuals but also targeted drug design of each disease. At the same time, the identification of sJSD signal biomarkers is also of great significance for studying the molecular mechanism of disease progression from a dynamic perspective.

No abstract

Over the past several decades, numerous scholars have studied the stability and Hopf bifurcation problem of integer-order delayed neural networks. However, the fruits about the stability and Hopf bifurcation for fractional-order delayed neural networks are very scarce. In this paper, we will consider the stability and the existence of Hopf bifurcation of fractional-order bidirectional associative memory (BAM) neural networks with four delays. A set of sufficient criteria to ensure the stability and the existence of Hopf bifurcation for the fractional-order BAM neural networks with four delays are established by choosing the sum of two different delays as a bifurcation parameter. This paper manifests that the delay has an important influence on the stability and Hopf bifurcation of involved networks. An example is displayed to test the rationality of the derived theoretical findings. The derived results of this paper are new and play a key role in optimizing networks and improving human life. INDEX TERMS BAM neural networks, stability, Hopf bifurcation, fractional order, delay.

No abstract