Related papers: Generating Markov evolutionary matrices for a give…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…
The evolutionary process has been modelled in many ways using both stochastic and deterministic models. We develop an algebraic model of evolution in a population of asexually reproducing organisms in which we represent a stochastic walk in…
We introduce a novel class of generative models based on piecewise deterministic Markov processes (PDMPs), a family of non-diffusive stochastic processes consisting of deterministic motion and random jumps at random times. Similarly to…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models…
A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter the resulting structure is worked out…
This work demonstrates how a complete statistical model quantifying the evolution of pairs of aligned proteins can be constructed from a time-parameterised substitution matrix and a time-parameterised 3-state alignment machine. All…
Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…
Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…
We consider a time-continuous Markov branching process of proliferating cells with a countable collection of types. Among-type transitions are inspired by the Tug-of-War process introduced in McFarland et al. as a mathematical model for…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
We consider a general class of branching processes in discrete time, where particles have types belonging to a Polish space and reproduce independently according to their type. If the process is critical and the mean distribution of types…
We consider a Markovian evolution on point processes, the $\Psi$--process, on the unit interval in which points are added according to a rule that depends only on the spacings of the existing point configuration. Having chosen a spacing, a…
We consider models for molecular sequence evolution in which the transition rates at each site depend on the local sequence context, giving rise to a time-inhomogeneous Markov process in which sites evolve under a complex dependency…
Let S be a denumerable state space and let P be a transition probability matrix on S. If a denumerable set M of nonnegative matrices is such that the sum of the matrices is equal to P, then we call M a partition of P. Let K denote the set…
We extend in two directions our previous results about the sampling and the empirical measures of immortal branching Markov processes. Direct applications to molecular biology are rigorous estimates of the mutation rates of polymerase chain…
Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are objects of different types. One field of application of such models in biology is in studies of cell proliferation. A sampling scheme…