AliSim: A Fast and Versatile Phylogenetic Sequence Simulator For the Genomic Era

Sequence simulators play an important role in phylogenetics. Simulated data has many applications, such as evaluating the performance of different methods, hypothesis testing with parametric bootstraps, and, more recently, generating data for training machine-learning applications. Many sequence simulation programs exist, but the most feature-rich programs tend to be rather slow, and the fastest programs tend to be feature-poor. Here, we introduce AliSim, a new tool that can efficiently simulate biologically realistic alignments under a large range of complex evolutionary models. To achieve high performance across a wide range of simulation conditions, AliSim implements an adaptive approach that combines the commonly-used rate matrix and probability matrix approach. AliSim takes 1.3 hours and 1.3 GB RAM to simulate alignments with one million sequences or sites, while popular software Seq-Gen, Dawg, and INDELible require two to five hours and 50 to 500 GB of RAM. We provide AliSim as an extension of the IQ-TREE software version 2.2, freely available at www.iqtree.org, and a comprehensive user tutorial at http://www.iqtree.org/doc/AliSim.

Prognostic Factors for Evolution of Non Alcoholic Fatty Liver Disease Patients Utilizing Poisson Regression and Continuous Time Markov Chains

In the present paper, the deleterious effects of obesity, type 2diabetes and insulin resistance, systolic and diastolic hypertension on the rate of progression of fibrosis in non-alcoholic fatty liver disease (NAFLD) patients are illustrated using a new approach utilizing the Poisson regression to model the transition rate matrix. The observed counts in the transition counts matrix are used as response variables and the covariates are the risk factors for fatty liver. Then the estimated counts from running the Poisson regression are used to estimate the transition rates using the continuous time Markov chains (CTMC) followed by exponentiation of the estimated rate matrix to obtain the transition probability matrix at specific time points. Using a hypothetical data of 150 participants followed up every year for a total of 28 years recording their demographic characteristics and their timeline of follow up are demonstrated. The findings revealed that insulin resistance expressed by MOMA-IR 2 has the most deleterious effects among other factors for increasing the rate of forward progression of patients from state 1 to state 2 as well as from state 2 to state 3 and from state 3 to state 4. The higher the level of HOMA-IR is, the more rapid the rate of progression is.

Prognostic Factors for Evolution of Non Alcoholic Fatty Liver Disease Patients Utilizing Poisson Regression and Continuous Time Markov Chains

In the present paper, the deleterious effects of obesity, type 2diabetes and insulin resistance, systolic and diastolic hypertension on the rate of progression of fibrosis in non-alcoholic fatty liver disease (NAFLD) patients are illustrated using a new approach utilizing the Poisson regression to model the transition rate matrix. The observed counts in the transition counts matrix are used as response variables and the covariates are the risk factors for fatty liver. Then the estimated counts from running the Poisson regression are used to estimate the transition rates using the continuous time Markov chains (CTMC) followed by exponentiation of the estimated rate matrix to obtain the transition probability matrix at specific time points. Using a hypothetical data of 150 participants followed up every year for a total of 28 years recording their demographic characteristics and their timeline of follow up are demonstrated. The findings revealed that insulin resistance expressed by MOMA-IR 2 has the most deleterious effects among other factors for increasing the rate of forward progression of patients from state 1 to state 2 as well as from state 2 to state 3 and from state 3 to state 4. The higher the level of HOMA-IR is, the more rapid the rate of progression is.

ADNOC's Smart Liner Initiative – A Step-Change in Matrix-Acid Stimulation Efficiency

ADNOC is progressing with large-scale rig-less high-rate matrix stimulation by deployment of advanced lower completions. A key contribution to future production growth is expected to come from these "Smart Liners" that rely on the principles of the limited-entry technique. The concept is based on a number of small, pre-drilled and unevenly spaced holes which enable an even distribution of acid along the entire reservoir drain to be stimulated. The smart liner incorporates swellable packers to avoid annular flow of acid to preferential zones and to isolate segments with heterogeneities. In this work, we focus on aspects related to planning, design and execution of high-rate matrix-acid stimulation of wells. We demonstrate that short wells need a different design approach compared to extended-reach wells and we provide guidelines on how to achieve the highest achievable pump rate and desired acid volume subject to reservoir, well and equipment constraints. The carbonate reservoirs typically exhibit considerable variation in permeability along the well, hence techniques for production profiling, such as inline tracers, are valuable for assessing the actual stimulation effectiveness. Wormhole penetration for a particular acid system will vary depending on the rock petrophysical properties and the reservoir properties; therefore, a systematic data analytics project is on-going.

The model-specific Markov embedding problem for symmetric group-based models

We study model embeddability, which is a variation of the famous embedding problem in probability theory, when apart from the requirement that the Markov matrix is the matrix exponential of a rate matrix, we additionally ask that the rate matrix follows the model structure. We provide a characterisation of model embeddable Markov matrices corresponding to symmetric group-based phylogenetic models. In particular, we provide necessary and sufficient conditions in terms of the eigenvalues of symmetric group-based matrices. To showcase our main result on model embeddability, we provide an application to hachimoji models, which are eight-state models for synthetic DNA. Moreover, our main result on model embeddability enables us to compute the volume of the set of model embeddable Markov matrices relative to the volume of other relevant sets of Markov matrices within the model.

Direct statistical inference for finite Markov jump processes via the matrix exponential

Given noisy, partial observations of a time-homogeneous, finite-statespace Markov chain, conceptually simple, direct statistical inference is available, in theory, via its rate matrix, or infinitesimal generator, $${\mathsf {Q}}$$ Q , since $$\exp ({\mathsf {Q}}t)$$ exp ( Q t ) is the transition matrix over time t. However, perhaps because of inadequate tools for matrix exponentiation in programming languages commonly used amongst statisticians or a belief that the necessary calculations are prohibitively expensive, statistical inference for continuous-time Markov chains with a large but finite state space is typically conducted via particle MCMC or other relatively complex inference schemes. When, as in many applications $${\mathsf {Q}}$$ Q arises from a reaction network, it is usually sparse. We describe variations on known algorithms which allow fast, robust and accurate evaluation of the product of a non-negative vector with the exponential of a large, sparse rate matrix. Our implementation uses relatively recently developed, efficient, linear algebra tools that take advantage of such sparsity. We demonstrate the straightforward statistical application of the key algorithm on a model for the mixing of two alleles in a population and on the Susceptible-Infectious-Removed epidemic model.

AN IMPROVEMENT OF MARKOVIAN INTEGRATION BY PARTS FORMULA AND APPLICATION TO SENSITIVITY COMPUTATION

This paper establishes a new version of integration by parts formula of Markov chains for sensitivity computation, under much lower restrictions than the existing researches. Our approach is more fundamental and applicable without using Girsanov theorem or Malliavin calculus as did by past papers. Numerically, we apply this formula to compute sensitivity regarding the transition rate matrix and compare with a recent research by an IPA (infinitesimal perturbation analysis) method and other approaches.

Phylosymmetric Algebras: Mathematical Properties of a New Tool in Phylogenetics

In phylogenetics, it is of interest for rate matrix sets to satisfy closure under matrix multiplication as this makes finding the set of corresponding transition matrices possible without having to compute matrix exponentials. It is also advantageous to have a small number of free parameters as this, in applications, will result in a reduction in computation time. We explore a method of building a rate matrix set from a rooted tree structure by assigning rates to internal tree nodes and states to the leaves, then defining the rate of change between two states as the rate assigned to the most recent common ancestor of those two states. We investigate the properties of these matrix sets from both a linear algebra and a graph theory perspective and show that any rate matrix set generated this way is closed under matrix multiplication. The consequences of setting two rates assigned to internal tree nodes to be equal are then considered. This methodology could be used to develop parameterised models of amino acid substitution which have a small number of parameters but convey biological meaning.