A Likelihood-Ratio Test for Lumpability of Phylogenetic Data: Is the Markovian Property of an Evolutionary Process Retained in Recoded DNA?

In molecular phylogenetics, it is typically assumed that the evolutionary process for DNA can be approximated by independent and identically distributed Markovian processes at the variable sites and that these processes diverge over the edges of a rooted bifurcating tree. Sometimes the nucleotides are transformed from a 4-state alphabet to a 3- or 2-state alphabet by a procedure that is called recoding, lumping, or grouping of states. Here, we introduce a likelihood-ratio test for lumpability for DNA that has diverged under different Markovian conditions, which assesses the assumption that the Markovian property of the evolutionary process over each edge is retained after recoding of the nucleotides. The test is derived and validated numerically on simulated data. To demonstrate the insights that can be gained by using the test, we assessed two published data sets, one of mitochondrial DNA from a phylogenetic study of the ratites and the other of nuclear DNA from a phylogenetic study of yeast. Our analysis of these data sets revealed that recoding of the DNA eliminated some of the compositional heterogeneity detected over the sequences. However, the Markovian property of the original evolutionary process was not retained by the recoding, leading to some significant distortions of edge lengths in reconstructed trees.[Evolutionary processes; likelihood-ratio test; lumpability; Markovian processes; Markov models; phylogeny; recoding of nucleotides.]

Ensemble mobility predictor based on random forest and Markovian property using LBSN data

The ubiquitous connectivity of Location-Based Systems (LBS) allows people to share individual location-related data anytime. In this sense, Location-Based Social Networks (LBSN) provides valuable information to be available in large-scale and low-cost fashion via traditional data collection methods. Moreover, this data contains spatial, temporal, and social features of user activity, enabling a system to predict user mobility. In this sense, mobility prediction plays crucial roles in urban planning, traffic forecasting, advertising, and recommendations, and has thus attracted lots of attention in the past decade. In this article, we introduce the Ensemble Random Forest-Markov (ERFM) mobility prediction model, a two-layer ensemble learner approach, in which the base learners are also ensemble learning models. In the inner layer, ERFM considers the Markovian property (memoryless) to build trajectories of different lengths, and the Random Forest algorithm to predict the user’s next location for each trajectory set. In the outer layer, the outputs from the first layer are aggregated based on the classification performance of each weak learner. The experimental results on the real user trajectory dataset highlight a higher accuracy and f1-score of ERFM compared to five state-of-the-art predictors.

A Markov chain-based feature extraction method for classification and identification of cancerous DNA sequences

Introduction: In recent decades, the growing rate of cancer incidence is a big concern for most societies. Due to the genetic origins of cancer disease, its internal structure is necessary for the study of this disease. Methods: In this research, cancer data are analyzed based on DNA sequences. The transition probability of occurring two pairs of nucleotides in DNA sequences has Markovian property. This property inspires the idea of feature dimension reduction of DNA sequence for overcoming the high computational overhead of genes analysis. This idea is utilized in this research based on the Markovian property of DNA sequences. This mapping decreases feature dimensions and conserves basic properties for discrimination of cancerous and non-cancerous genes. Results: The results showed that a non-linear support vector machine (SVM) classifier with RBF and polynomial kernel functions can discriminate selected cancerous samples from non-cancerous ones. Experimental results based on the 10-fold cross-validation and accuracy metrics verified that the proposed method has low computational overhead and high accuracy. Conclusion: The proposed algorithm was successfully tested on related research case studies. In general, a combination of proposed Markovian-based feature reduction and non-linear SVM classifier can be considered as one of the best methods for discrimination of cancerous and non-cancerous genes.

Stochastic Hydrology: Is Scientific Understanding Growing?

Among many problems of stochastic hydrology, several major problems may be singled out. (1) The methodology problem – may fluctuation of hydro-meteorological values be considered within the framework of probabilities and random processes? Was this topic discussed after 1953? (2) One-dimensional probability distributions – is there progress? Are there new models? (3) Random Processes: Is Markovian property sufficient or more complex models with memory are needed? (4) Lack of stability resulting from climate changes: Is there progress in understanding the approaches to probabilistic forecasts?

Reliability assessment of system under a generalized run shock model

In this paper we are concerned with modelling the reliability of a system subject to external shocks. In a run shock model, the system fails when a sequence of shocks above a threshold arrive in succession. Nevertheless, using a single threshold to measure the severity of a shock is too critical in real practice. To this end, we develop a generalized run shock model with two thresholds. We employ a phase-type distribution to model the damage size and the inter-arrival time of shocks, which is highly versatile and may be used to model many quantitative features of random phenomenon. Furthermore, we use the Markovian property to construct a multi-state system which degrades with the arrival of shocks. We also provide a numerical example to illustrate our results.

Choosing the number of groups in a latent stochastic blockmodel for dynamic networks

Latent stochastic blockmodels are flexible statistical models that are widely used in social network analysis. In recent years, efforts have been made to extend these models to temporal dynamic networks, whereby the connections between nodes are observed at a number of different times. In this paper, we propose a new Bayesian framework to characterize the construction of connections. We rely on a Markovian property to describe the evolution of nodes' cluster memberships over time. We recast the problem of clustering the nodes of the network into a model-based context, showing that the integrated completed likelihood can be evaluated analytically for a number of likelihood models. Then, we propose a scalable greedy algorithm to maximize this quantity, thereby estimating both the optimal partition and the ideal number of groups in a single inferential framework. Finally, we propose applications of our methodology to both real and artificial datasets.