25 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…
Rodrigo Cofré, Leonardo Videla, Fernando Rosas
Although most biological processes are characterized by a strong temporal asymmetry, several popular mathematical models neglect this issue. Maximum entropy methods provide a principled way of addressing time irreversibility, which leverages powerful results and ideas from the literature of non-equilibrium statistical…
Juan Kuntz
What this book is intended to be. Even though I've disguised it very well, this book is actually written for those interested in the applications of Markov chains (discrete-time and continuous-time processes that satisfy the Markov property and take values in countable sets). I have two main goals in writing it:
Jeffrey J. Hunter
In a finite m-state irreducible Markov chain with stationary probabilities {πi} and mean first passage times mij (mean recurrence time when i = j) Kemeny and Snell, (1960), showed that π j j=1 m ∑ mij is a constant, K, not depending on i. This constant has since become known as Kemeny's constant. Interest in this…
Ricardo Frumento
| 1 | Abstract | | 1 | | --- | --- | --- | --- | | 2 | Motivation | | 1 | | | 2.1 | Stochastic Systems | 1 | | | 2.2 Markov Chains | | 2 | | 3 | Description and Solution | | 2 | | | 3.1 | Initial Assumptions | 2 | | | 3.2 | Solving a System | 2 | | 4 | Discussion | | 5 | | 5 | Conclusion | | 5 | | | Bibliography | | 5…
Marcus Kaiser, Robert L. Jack, Johannes Zimmer
We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a non-linear relation between probability currents and…
Jianhong Xu
It is well known that any higher order Markov chain can be associated with a first order Markov chain. In this primarily expository article, we present the first fairly comprehensive analysis of the relationship between higher order and first order Markov chains, together with illustrative examples. Our main objective…
Isaac J. Sledge, José C. Príncipe
In this paper, we propose an approach to obtain reduced-order models of Markov chains. Our approach is composed of two information-theoretic processes. The first is a means of comparing pairs of stationary chains on different state spaces, which is done via the negative, modified Kullback-Leibler divergence defined on…
Vahid Moosavi, Giulio Isacchini, Rodrigo Huerta-Quintanilla
The initial theoretical connections between Leontief input-output models and Markov chains were established back in 1950s. However, considering the wide variety of mathematical properties of Markov chains, so far there has not been a full investigation of evolving world economic networks with Markov chain formalism. In…
Ernest Nieznaj, Nikolai Leonenko
We consider a Markov chain that can be termed a discrete version of Blackwell’s example from 1958. It is constructed with the aid of a sequence of independent Markov chains with two states. It turns out its stationary distribution $π$ and transition matrix P are in detailed balance. As a result, the transition operator…
Michael Gr. Voskoglou
Markov chains offer ideal conditions for the study and mathematical modelling of a certain kind of situations depending on random variables. The basic concepts of the corresponding theory were introduced by Markov in 1907 on coding literary texts. Since then, the Markov chain theory was developed by a number of leading…
Soumik Pal, Tim Mesikepp
We close this section by saying further examination of Brownian motion is beyond the scope of our text, but we hope this very brief introduction has whetted your appetite to study it further in the future. The simple random walk on Z is fundamentally important, but other variations occur in theory and practice. One…
Zhihang Peng, Changjun Bao, Yang Zhao, Honggang Yi + 4 more
'Hao Yu' 'Hongbing Shen' 'Feng Chen'] This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course. Then the paper presents a weighted Markov chain, a method…
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…
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…
Lorenzo Facciaroni, Costantino Ricciuti, Enrico Scalas, Bruno Toaldo
There is a well-established theory that links semi-Markov chains having Mittag-Leffler waiting times to time-fractional equations. We here go beyond the semi-Markov setting, by defining some non-Markovian chains whose waiting times, although marginally Mittag-Leffler, are assumed to be stochastically dependent. This…
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…
Authors not listed
Sequence is the critical determinant of macromolecular function, yet current polymer design approaches often optimize monomer composition and ratios while ignoring sequence. This creates poorly defined design spaces for active learning that miss the vast combinatorial landscape of sequence possibilities. We introduce…
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…
Robert Arbon, Yanchen Zhu, Antonia S. J. S. Mey
Markov state models (MSM) are a popular statistical method for analyzing the conformational dynamics of proteins, including protein folding. With all statistical and machine learning (ML) models choices must be made about the modeling pipeline that cannot be directly learned from the data. These choices, or…
Anupam Ojha, Saumya Thakur, Surl-Hee Ahn, Rommie Amaro
Recent advances in computational power and algorithms have made molecular dynamics (MD) simulations reach greater timescales. However, for observing conformational transitions associated with biomolecular processes, MD simulations still have limitations. Several enhanced sampling techniques seek to address this…
Anupam Ojha, Saumya Thakur, Surl-Hee Ahn, Rommie Amaro
Recent advances in computational power and algorithms have made molecular dynamics (MD) simulations reach greater timescales. However, for observing conformational transitions associated with biomolecular processes, MD simulations still have limitations. Several enhanced sampling techniques seek to address this…
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…
Tim Marshall, Robert Raddi, Vincent Voelz
All-atom molecular dynamics (MD) simulations can provide detailed insight into a molecule's conformational ensemble in solution. While molecular force fields are parameterized to accurately model a protein's potential energy surface, it remains challenging in practice to evaluate how well force fields can capture…
Ben Humphries, Joshua Kinslow, Dale Green, Garth Jones
Open quantum systems often operate in the non-Markovian regime where a finite history of a trajectory is intrinsic to its evolution. The degree of non-Markovianity for a trajectory may be measured in terms of the amount of information flowing from the bath back into the system. In this study we consider how information…