Related papers: An exact multiple-time-step variational formulatio…
Two quantum systems, each described as a random-matrix ensemble. are coupled to each other via a number of transition states. Each system is strongly coupled to a large number of channels. The average transmission probability is the product…
Given a random walk a method is presented to produce a matrix of transition probabilities that is consistent with that random walk. The method is a kind of reverse application of the usual ergodicity and is tested by using a transition…
Dynamic logit models are popular tools in economics to measure state dependence. This paper introduces a new method to derive moment restrictions in a large class of such models with strictly exogenous regressors and fixed effects. We…
Compounding error, where small prediction mistakes accumulate over time, presents a major challenge in learning-based control. A common remedy is to train multi-step predictors directly instead of rolling out single-step models. However, it…
Transitional localised turbulence in shear flows is known to either decay to an absorbing laminar state or proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number…
We propose a data-driven optimization-based pre-compensation method to improve the contour tracking performance of precision motion stages by modifying the reference trajectory and without modifying any built-in low-level controllers. The…
In this article we use geometric optimal control to completely solve the problem of minimum-time transitions between thermal equilibrium and fixed average energy states of the quantum parametric oscillator, a system which has been…
Migration between different habitats is ubiquitous among biological populations. In this Letter, we study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way…
The typical central limit theorems in high-frequency asymptotics for semimartingales are results on stable convergence to a mixed normal limit with an unknown conditional variance. Estimating this conditional variance usually is a hard…
In this note, we address formally the issue of symmetry for probabilities of different dynamical pathways in the forward and reverse directions of a conformational transition. Our discussion is based on a decomposition of equilibrium into…
This letter proposes a predictor-corrector method to strike a balance between simulation accuracy and efficiency by appropriately tuning the numerical integration step length of a power system time-domain simulation. Numerical tests…
In this paper, we present a novel iterative Monte Carlo method for approximating the stationary probability of a single state of a positive recurrent Markov chain. We utilize the characterization that the stationary probability of a state…
We prove several results about the rate of convergence to stationarity, that is, the spectral gap, for the M/M/n queue in the Halfin-Whitt regime. We identify the limiting rate of convergence to steady-state, and discover an asymptotic…
Transformers have proven highly effective across various applications, especially in handling sequential data such as natural languages and time series. However, transformer models often lack clear interpretability, and the success of…
We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and…
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…
We consider a high-$Q$ Duffing oscillator in a weakly non-linear regime with the driving frequency $\sigma$ varying in time between $\sigma_i$ and $\sigma_f$ at a characteristic rate $r$. We found that the frequency sweep can cause…
We analyze the rates of noise-induced transitions between period-two attractors. The model investigated is an underdamped oscillator parametrically driven by a field at nearly twice the oscillator eigenfrequency. The activation energy of…
We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum…
Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…