14 papers · ranked by Valyu relevance
Kyu Hyong Park, Réka Albert
Comprehensive analysis of the dynamics of Boolean models of biological systems is hampered by the exponentially large state space. Here we introduce the succession-diagram-based Markov chain (SD Markov chain), a coarse-grained representation that uses trap spaces (unescapable state subspaces) of the Boolean model as…
Jordan M Culp, Donovan M Ashby, Antis G George, G. Campbell Teskey + 2 more
Mesoscale cortical dynamics consist of stereotyped patterns of recurring activity motifs, however the constraints and rules governing how these motifs assemble over time is not known. Here we propose a Continuous Time Markov Chain model that probabilistically describes the temporal sequence of activity motifs using…
Joel Valdivia Ortega
Today we are able to describe genome evolution but, there are still several open questions on this area such as: Which is the probability that a mutation occurs at a nucleotide level? Is it possible to predict the evolution of a particular genome?, or talking about preservation, is there a way to simulate the genetic…
Ulrich K. Steiner, Shripad Tuljapurkar
Individuals differ greatly in their life courses, but how such diversity is generated, how it has evolved and how it is maintained is less understood. However, such understanding is crucial to comprehend evolutionary and ecological population dynamics. In structured populations individuals diversify by transitioning…
John J. Vastola, Tejas Ramdas, Samuel J. Gershman
Cells store information in part by attaching molecular marks to proteins and DNA. But because marks can be randomly removed (e.g., due to ambient phosphatase activity) and added (e.g., due to ambient kinase activity), information encoding may be poor, and in the worst case marks may only store information on the time…
V.P. Skornyakov, M.V. Skornyakova, A.V. Shurygina, P.V. Skornyakov
In this study Markov chain models of gene regulatory networks (GRN) are developed. These models gives the ability to apply the well known theory and tools of Markov chains to GRN analysis. We introduce a new kind of the finite graph of the interactions called the combinatorial net that formally represent a GRN and the…
Joel Valdivia Ortega
Today we are able to describe genome evolution but, there are still several open questions on this area such as: Which is the probability that a mutation occurs at a nucleotide level? Is it possible to predict the evolution of a particular genome?, or talking about preservation, is there a way to simulate the genetic…
David H. Margarit, Marcela V. Reale, Ariel F. Scagliotti, Lilia M. Romanelli
Absorbing Markov Chains are an important mathematical tool used for different applications in science. On the other hand, cancer and its metastases in children have a significant impact on health due to their degree of lethality. Therefore, the aim of this work is to model the metastatic pathways of the main childhood…
Ernesto Suárez, Rafal P. Wiewiora, Chris Wehmeyer, Frank Noé + 2 more
Markov state models (MSMs) have been widely applied to study the kinetics and pathways of protein conformational dynamics based on statistical analysis of molecular dynamics (MD) simulations. These MSMs coarse-grain both configuration space and time in ways that limit what kinds of observables they can reproduce with…
Cheng Hao, Garrick Dorian, Rohan Fernando
Bayesian multiple regression methods are widely used in whole-genome analyses to solve the problem that the number p of marker covariates is usually larger than the number n of observations. Inferences from most Bayesian methods are based on Markov chain Monte Carlo methods, where statistics are computed from a Markov…
Kevin Song, Dmitrii E. Makarov, Etienne Vouga
A key theoretical challenge posed by single-molecule studies is the inverse problem of deducing the underlying molecular dynamics from the time evolution of low-dimensional experimental observables. Toward this goal, a variety of low-dimensional models have been proposed as descriptions of single-molecule signals…
Rebecca K. Borchering, Scott A. McKinley
In the last decade there has been growing criticism of the use of Stochastic Differential Equations (SDEs) to approximate discrete state-space, continuous-time Markov chain population models. In particular, several authors have demonstrated the failure of Diffusion Approximation, as it is often called, to approximate…
Ian Holmes
We introduce a systematic method of approximating finite-time transition probabilities for continuous-time insertion-deletion models on sequences. The method uses automata theory to describe the action of an infinitesimal evolutionary generator on a probability distribution over alignments, where both the generator and…
Curtis Goolsby, Mahmoud Moradi
Markov State Models (MSM) and related techniques have gained significant traction as a tool for analyzing and guiding molecular dynamics (MD) simulations due to their ability to extract structural, thermodynamic, and kinetic information on proteins using computationally feasible MD simulations. The MSM analysis often…