Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-steppingmethod to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods ...

In reinforcement learning, the TD(λ) algorithm is a fundamental policy evaluation method with an efficient online implementation that is suitable for large-scale problems. One practical drawback of TD(λ) is its sensitivity to the choice of the step-size. It is an empirically well-known fact that a large step-size leads to fast convergence, at the cost of higher variance and risk of instability....

In this study, a numerical solution of 2D steady incompressible lid-driven cavity flow is presented. Three different numerical schemes were employed to make a comparison on the practicality of the methods. An alternating direction implicit scheme for the vorticity-stream function formulation, explicit and implicit schemes for the primitive variable formulation of governing Navier-Stokes equatio...

We discuss nonperturbative radiation for a recently introduced class of infrared safe event shape weights, which describe the narrow-jet limit. Starting from next-to-leading logarithmic (NLL) resummation, we derive an approximate scaling rule that relates the nonperturbative shape functions for these weights to the shape function for the thrust. We argue that the scaling reflects the boost inva...

We have investigated the absorption and emission spectrum of 5-hydroxyindole in the gas phase and in various solvents. 5-Hydroxyindole is the fluorophore of the non-natural amino acid 5-hydroxytryptophan, which has attracted recent interest as a novel intrinsic probe for protein structure, dynamics, and function. Gas-phase and implicit solvent calculations were performed with multiconfiguration...

We consider differential delay equations of the form $\partial_tx(t) = X_{t}(x(t - \tau))$ in $\mathbb{R}^n$, where $(X_t)_{t\in S^1}$ is a time-dependent family smooth vector fields on $\mathbb{R}^n$ and $\tau$ parameter. If there (suitably non-degenerate) periodic solution $x_0$ this equation for $\tau=0$, that without delay, are good reasons to expect existence solutions all sufficiently sma...