Hidden Markov models (HMMs) provide an excellent analysis of recordings with very poor signal/noise ratio made from systems such as ion channels which switch among a few states. This method has also recently been used for modeling the kinetic rate constants of molecular motors, where the observable variable-the position-steadily accumulates as a result of the motor's reaction cycle. We present ...

We consider an incremental gradient method with momentum term for minimizing the sum of continuously differentiable functions. This method uses a new adaptive stepsize rule that decreases the stepsize whenever sufficient progress is not made. We show that if the gradients of the functions are bounded and Lipschitz continuous over a certain level set, then every cluster point of the iterates gen...

Some previous works show that symmetric fixedand variablestepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts,...

Volterra integro-differential equations with time-dependent delay arguments (DVIDEs) can provide us with realistic models of many real-world phenomena. Delayed LoktaVolterra predator-prey systems arise in Ecology and are well-known examples of DVIDEs first introduced by Volterra in 1928. We investigate the numerical solution of systems of DVIDEs using an adaptive stepsize selection strategy. We...

Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators desirable their stability properties, significantly relaxing restrictions on timestep size. However, implicit require solutions to one or more systems nonlinear equations at each timestep, which large simulations can be prohibitively ex...

We consider variable stepsize time approximations of holomorphic semigroups on general Banach spaces. For strongly A(0)-acceptable rational functions a general stability theorem is proved, which does not impose any constraint on the ratios between stepsizes.

The numerical integration of reversible dynamical systems is considered. A backward analysis for variable stepsize one-step methods is developed, and it is shown that the numerical solution of a symmetric one-step method, implemented with a reversible stepsize strategy, is formally equal to the exact solution of a perturbed differential equation, which again is reversible. This explains geometr...

The aim of this talk is to present highly stable collocation based numerical methods for Volterra Integral Equations (VIEs). As it is well known, a collocation method is based on the idea of approximating the exact solution of a given integral equation with a suitable function belonging to a chosen finite dimensional space, usually a piecewise algebraic polynomial, which satisfies the integral ...