Related papers: Using Markov State Models to Study Self-Assembly
Understanding the dynamic behavior of biomolecules is fundamental to elucidating biological function and facilitating drug discovery. While Molecular Dynamics (MD) simulations provide a rigorous physical basis for studying these dynamics,…
We consider Markov models of stochastic processes where the next-step conditional distribution is defined by a kernel density estimator (KDE), similar to Markov forecast densities and certain time-series bootstrap schemes. The KDE Markov…
MCMC methods (Monte Carlo Markov Chain) are a class of methods used to perform simulations per a probability distribution $P$. These methods are often used when we have difficulties to directly sample per a given probability distribution…
The main subject of the thesis is the study of stationary nonequilibrium states trough the use of microscopic stochastic models that encode the physical interaction in the rules of Markovian dynamics for particles configurations. These…
Recently, there has been a surge of interest in using spectral methods for estimating latent variable models. However, it is usually assumed that the distribution of the observations conditioned on the latent variables is either discrete or…
Hidden Markov models (HMMs) and their extensions have proven to be powerful tools for classification of observations that stem from systems with temporal dependence as they take into account that observations close in time are likely…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
In the case of a linear state space model, we implement an MCMC sampler with two phases. In the learning phase, a self-tuning sampler is used to learn the parameter mean and covariance structure. In the estimation phase, the parameter mean…
Understanding the behavior of complex molecular systems is a fundamental problem in physical chemistry. To describe the long-time dynamics of such systems, which is responsible for their most informative characteristics, we can identify a…
Markov networks are frequently used in sciences to represent conditional independence relationships underlying observed variables arising from a complex system. It is often of interest to understand how an underlying network differs between…
State Space Models (SSMs), developed to tackle long sequence modeling tasks efficiently, offer both parallelizable training and fast inference. At their core are recurrent dynamical systems that maintain a hidden state, with update costs…
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…
We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing one. In particular, we may start with a superprocess,…
The formation and regulation of macromolecular complexes provides the backbone of most cellular processes, including gene regulation and signal transduction. The inherent complexity of assembling macromolecular structures makes current…
Markov processes are popular mathematical models, studied by theoreticians for their intriguing properties, and applied by practitioners for their flexible structure. With this book we teach how to model and analyze Markov processes. We…
Hidden Markov models (HMMs) offer a robust and efficient framework for analyzing time series data, modelling both the underlying latent state progression over time and the observation process, conditional on the latent state. However, a…
A plethora of protein language models have been released in recent years. Yet comparatively little work has addressed how to best sample from them to optimize desired biological properties. We fill this gap by proposing a flexible,…
We present a generic computational framework for the simulation of viral capsid assembly which is quantitative and specific. Starting from PDB files containing atomic coordinates, the algorithm builds a coarse grained description of protein…
This paper introduces new efficient algorithms for two problems: sampling conditional on vertex degrees in unweighted graphs, and sampling conditional on vertex strengths in weighted graphs. The algorithms can sample conditional on the…
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…