A brief introduction to discrete variational mechanics, motivated by the goal of constructing symplectic onestep methods, will be presented. Followed by the presentation of a new type of variational integrator that utilizes Taylor’s method in it’s construction. Time permitting, we will make some remarks on the pros/cons and stability of constructing the variational integrator from the Lagrangia...

This research paper examines the derivation and implementation of a new 4-point block method for direct integration of first-order ordinary differential equations using interpolation and collocation techniques. The approximate solution is a combination of power series and exponential function. The paper further investigates the properties of the new integrator and found it to be zero-stable, co...

A sigma delta modulator incorporating a linear phase integrator instead of a conventional voltage-domain integrator is described. The architecture allows achieving a quasi-second order noise shaping by using a passive SC low-pass filter in the first stage. Simulation results demonstrate that the circuit can operate with sampling frequencies of hundred of MHz while obtaining a figure of merit (F...

We investigated a model for the neural integrator based on hysteretic units connected by positive feedback. Hysteresis is assumed to emerge from the intrinsic properties of the cells. We consider the recurrent networks containing either bistable or multistable neurons. We apply our analysis to the oculomotor velocity-to-position neural integrator that calculates eye positions using the inputs t...