many natural and real-world applications, the measured signals are controlled by underlying processes or drivers. As a result, these signals exhibit highly redundant representations and their temporal evolution can be compactly described by a dynamical process on a low-dimensional manifold. In this paper, we propose a graph-based method for revealing the low-dimensional manifold and inferring t...

In this paper, we combine the recent findings in robust topology optimization formulations and partial differential equation based density filtering to improve the topological design of electromechanical actuators. For the electromechanical analysis, we adopt a monolithic formulation to model the coupled electrostatic and mechanical equations. For filtering, we extend the Helmholtz-based projec...

We consider the incompressible Navier-Stokes equations with spatially periodic boundary conditions. If the Reynolds number is small enough we provide an elementary short proof of the existence of global in time Hölder continuous solutions. Our proof is based on the stochastic Lagrangian formulation of the Navier-Stokes equations, and works in both the two and three dimensional situation.

For the Kuramoto Sivashinsky equation with L-periodic boundary conditions we show that the radius of space analyticity on the global attractor is lowersemicontinuous function at the stationary solutions, and thereby deduce the existence of a neighborhood in the global attractor of the set of all stationary solutions in which the radius of analyticity is independent of the bifurcation parameter ...

ARCH/GARCH modelling has been successfully applied in empirical finance for many years. This paper surveys the semiparametric and nonparametric methods in univariate andmultivariate ARCH/GARCHmodels. First, we introduce some specific semiparametric models and investigate the semiparametric and nonparametrics estimation techniques applied to: the error density, the functional form of the volatil...

The behaviour of extended particles with exclusion interaction on a one-dimensional lattice is investigated. The basic model is called ℓ-ASEP as a generalization of the asymmetric exclusion process (ASEP) to particles of arbitrary length ℓ. Stationary and dynamical properties of the ℓ-ASEP with periodic boundary conditions are derived in the hydrodynamic limit from microscopic properties of the...

This paper presents a method to verify closed-loop properties of optimizationbased controllers for deterministic and stochastic constrained polynomial discrete-time dynamical systems. The closed-loop properties amenable to the proposed technique include global and local stability, performance with respect to a given cost function (both in a deterministic and stochastic setting) and the L2 gain....