Related papers: Statistics of trajectories in two-state master equ…
This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this…
We introduce a representation learning framework for spatial trajectories. We represent partial observations of trajectories as probability distributions in a learned latent space, which characterize the uncertainty about unobserved parts…
We use projected entangled-pair states (PEPS) to calculate the large deviations (LD) statistics of the dynamical activity of the two dimensional East model, and the two dimensional symmetric simple exclusion process (SSEP) with open…
The evolution of a continuous time Markov process with a finite number of states is usually calculated by the Master equation - a linear differential equations with a singular generator matrix. We derive a general method for reducing the…
We describe a robust and efficient chain-of-states method for computing Minimum Energy Paths~(MEPs) associated to barrier-crossing events in poly-atomic systems. The path is parametrized in terms of a continuous variable $t \in [0,1]$ that…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
The rate of escape of an ideal bead-spring polymer in a symmetric double-well potential is calculated using transition state theory (TST) and the results compared with direct dynamical simulations. The minimum energy path of the transitions…
We study the trajectories of a single colloidal particle as it hops between two energy wells A and B, which are sculpted using adjacent optical traps by controlling their respective power levels and separation. Whereas the dynamical…
We provide a unified picture for the master equation approach and the quantum trajectory approach to a measurement problem of a two-state quantum system (a qubit), an electron coherently tunneling between two coupled quantum dots (CQD's)…
This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only…
We present an efficient method to compute transition rates between states for a two-state system. The method utilizes the equivalence between steady-state flux and mean first passage rate for such systems. More specifically, the procedure…
Transition path sampling is a method for estimating the rates of rare events in molecular systems based on the gradual transformation of a path distribution containing a small fraction of reactive trajectories into a biased distribution in…
We propose a general method for simplifying master equations by eliminating from the description rapidly evolving states. The physical recipe we impose is the suppression of these states and a renormalization of the rates of all the…
The steady states of the master equation are investigated. We give two expressions for the steady state distribution of the master equation a la the Zubarev-McLennan steady state distribution, i.e., the exact expression and an expression…
A method to generate reactive trajectories, namely equilibrium trajectories leaving a metastable state and ending in another one is proposed. The algorithm is based on simulating in parallel many copies of the system, and selecting the…
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time ). The…
In this note we derive the exact probability that a specific state in a two-state Markov chain is visited exactly $k$ times after $N$ transitions. We provide a closed-form solution for $\mathbb{P}(N_l = k \mid N)$, considering initial state…
A deterministic temporal process can be determined by its trajectory, an element in the product space of (a) initial condition $z_0 \in \mathcal{Z}$ and (b) transition function $f: (\mathcal{Z}, \mathcal{T}) \to \mathcal{Z}$ often…
A new representation of the exact time dependent solution of the discrete master equation is derived. This representation can be considered as contraction of the path integral solution of Haken. It allows the calculation of the probability…
Getting tools that allow simple representations and comparisons of a set of categorical trajectories is of major interest for statisticians. Without loosing any information, we associate to each state a binary random indicator function,…