In the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional Fredholm integral equations of the second kind‎. ‎The solution of the‎ integral equation is described by the Neumann series expansion‎. ‎Each term of this expansion can be considered as an expectation which is approximated by a continuous Markov chain Monte Carlo method‎. ‎An algorithm is proposed to sim...

In this article, we treat extended balancing for continuous-time linear time-invariant systems. We take a dissipativity perspective, thus, resulting in characterization terms of matrix inequalities. This perspective is useful determining priori error bounds. addition, address the problem structure-preserving model reduction subclass port-Hamiltonian establish sufficient conditions to ensure tha...

It is often useful to model the behavior of an autonomous intelligent creature in terms of continuous control and choice. For example, a robot who moves through space can be idealized as able to execute any continuous motion, subject to constraints on velocity and accelleration; in such a model, the robot can %hoose = at any instant to change his accelleration. We show how such models can be de...

The DSSP program assigns protein secondary structure to one of eight states. This discrete assignment cannot describe the continuum of thermal fluctuations. Hence, a continuous assignment is proposed. Technically, the continuum results from averaging over ten discrete DSSP assignments with different hydrogen bond thresholds. The final continuous assignment for a single NMR model successfully re...