Background Biological age (BA) is a more accurate measure of the rate of human aging than chronological age (CA). However, there is limited consensus regarding measures of BA in life span and healthspan. Methods This study investigated measurement sets of 68 physiological biomarkers using data from 2,844 Chinese Singaporeans in two age subgroups (55–70 and 71–94 years) in the Singapore Longitudinal Aging Study (SLAS-2) with 8-year follow-up frailty and mortality data. We computed BA estimate using three commonly used algorithms: Principal Component Analysis (PCA), Multiple Linear Regression (MLR), and Klemera and Doubal (KD) method, and additionally, explored the use of machine learning methods for prediction of mortality and frailty. The most optimal algorithmic estimate of BA compared to CA was evaluated for their associations with risk factors and health outcome. Results Stepwise selection procedures resulted in the final selection of 8 biomarkers in males and 10 biomarkers in females. The highest-ranking biomarkers were estimated glomerular filtration rate for both genders, and the forced expiratory volume in 1 second in males and females. The BA estimates robustly predicted frailty and mortality and outperformed CA. The best performing KD measure of BA was notably predictive in the younger group (aged 55–70 years). BA estimates obtained using a machine learning train-test method were not more accurate than conventional BA estimates in predicting mortality and frailty in most situations. Biologically older people with the same CA as biologically younger individuals had higher prevalence of frailty and 8-year mortality, and worse health, behavioral, and functional characteristics. Conclusions BA is better than CA for measuring life span (mortality) and healthspan (frailty). This measurement set of physiological markers of biological aging among Chinese robustly differentiate biologically old from younger individuals with the same CA.

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Interdependent networks in areas ranging from infrastructure to economics are ubiquitous in our society, and the study of their cascading behaviors using percolation theory has attracted much attention in recent years. To analyze the percolation phenomena of these systems, different mathematical frameworks have been proposed, including generating functions and eigenvalues, and others. These different frameworks approach phase transition behaviors from different angles and have been very successful in shaping the different quantities of interest, including critical threshold, size of the giant component, order of phase transition, and the dynamics of cascading. These methods also vary in their mathematical complexity in dealing with interdependent networks that have additional complexity in terms of the correlation among different layers of networks or links. In this work, we review a particular approach of simple, self-consistent probability equations, and we illustrate that this approach can greatly simplify the mathematical analysis for systems ranging from single-layer network to various different interdependent networks. We give an overview of the detailed framework to study the nature of the critical phase transition, the value of the critical threshold, and the size of the giant component for these different systems. c − , of nodes are removed. If that happens, then the largest cluster, which is known as the giant component, disappears and all of the clusters become negligibly small. This phase is associated with the disintegration of the network. Therefore, the size, μ ∞ , of the giant component serves as an order parameter that is very useful in studying the phase transition behaviors and the robustness of the network structure.Some original works [1,15] provided a precise and powerful analytical solution to the phase transition behaviors. In their mathematical analysis, recursive mapping was used to track the percolation process in each stage of cascading failures. In some systems where correlations exist in dependency links [7-9, 16, 17], this method, while having the advantage of following and yielding insight into the cascading process [18], could lead OPEN ACCESS RECEIVED

Human gene regulatory networks (GRN) can be difficult to interpret due to a tangle of edges interconnecting thousands of genes. We constructed a general human GRN from extensive transcription factor and microRNA target data obtained from public databases. In a subnetwork of this GRN that is active during estrogen stimulation of MCF-7 breast cancer cells, we benchmarked automated algorithms for identifying core regulatory genes (transcription factors and microRNAs). Among these algorithms, we identified K-core decomposition, pagerank and betweenness centrality algorithms as the most effective for discovering core regulatory genes in the network evaluated based on previously known roles of these genes in MCF-7 biology as well as in their ability to explain the up or down expression status of up to 70% of the remaining genes. Finally, we validated the use of K-core algorithm for organizing the GRN in an easier to interpret layered hierarchy where more influential regulatory genes percolate towards the inner layers. The integrated human gene and miRNA network and software used in this study are provided as supplementary materials (S1 Data) accompanying this manuscript.