Related papers: Modelling ion channels with a view towards identif…
It is shown that the exact dynamics of a composite quantum system can be represented through a pair of product states which evolve according to a Markovian random jump process. This representation is used to design a general Monte Carlo…
It has long been accepted that the multiple-ion single-file transport model is appropriate for many kinds of ion channels. However, most of the purely theoretical works in this field did not capture all of the important features of the…
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…
We propose a collision model to investigate the information dynamics of a system coupled to an environment with varying degrees of non-Markovianity. We control the degree of non-Markovianity by applying a depolarising channel to a fixed and…
Motivated by applications in movement ecology, in this paper I propose a new class of integrated continuous-time hidden Markov models in which each observation depends on the underlying state of the process over the whole interval since the…
Jump Markov linear models consists of a finite number of linear state space models and a discrete variable encoding the jumps (or switches) between the different linear models. Identifying jump Markov linear models makes for a challenging…
Panel data, also known as longitudinal data, consist of a collection of time series. Each time series, which could itself be multivariate, comprises a sequence of measurements taken on a distinct unit. Mechanistic modeling involves writing…
Markov chains are simple yet powerful mathematical structures to model temporally dependent processes. They generally assume stationary data, i.e., fixed transition probabilities between observations/states. However, live, real-world…
State-space models are commonly used to describe different forms of ecological data. We consider the case of count data with observation errors. For such data the system process is typically multi-dimensional consisting of coupled Markov…
A fundamental problem when aggregating Markov chains is the specification of the number of state groups. Too few state groups may fail to sufficiently capture the pertinent dynamics of the original, high-order Markov chain. Too many state…
Ionic models, the set of ordinary differential equations (ODEs) describing the time evolution of the state of excitable cells, are the cornerstone of modeling in neuro- and cardiac electrophysiology. Modern ionic models can have tens of…
Gene regulatory networks with dynamics characterized by multiple stable states underlie cell fate-decisions. Quantitative models that can link molecular-level knowledge of gene regulation to a global understanding of network dynamics have…
A periodically modulated N-state model whose dynamics is governed by a time-convoluted generalized master equation is theoretically analyzed. It is shown that this non-Markovian master equation can be converted to a Markovian master…
This chapter reviews how molecular dynamics simulations, experimental data, and Markov state models can synergize to map-out the mechanism of protein-protein association and dissociation.
Conventional joint modeling approaches generally characterize the relationship between longitudinal biomarkers and discrete event occurrences within terminal, recurring or competing risk settings, thereby offering a limited representation…
The availability of relational data can offer new insights into the functioning of the economy. Nevertheless, modeling the dynamics in network data with multiple types of relationships is still a challenging issue. Stochastic block models…
In this article a flexible Bayesian non-parametric model is proposed for non-homogeneous hidden Markov models. The model is developed through the amalgamation of the ideas of hidden Markov models and predictor dependent stick-breaking…
Time series of conformational dynamics in proteins are usually evaluated with hidden Markov models (HMMs). This approach works well if the number of states and their connectivity is known. However, for the multi-domain protein Hsp90, a…
Probabilistic generative models based on measure transport, such as diffusion and flow-based models, are often formulated in the language of Markovian stochastic dynamics, where the choice of the underlying process impacts both algorithmic…
It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…