Outputs and time lags for linear bioreactors

Learning Over Long Time Lags

The advantage of recurrent neural networks (RNNs) in learning dependencies between time-series data has distinguished RNNs from other deep learning models. Recently, many advances are proposed in this emerging field. However, there is a lack of comprehensive review on memory models in RNNs in the literature. This paper provides a fundamental review on RNNs and long short term memory (LSTM) mode...

Polynomial-time approximation schemes for scheduling problems with time lags

We identify two classes of machine scheduling problems with time lags that possess Polynomial-Time Approximation Schemes (PTASs). These classes together, one for minimizing makespan and one for minimizing total completion time, include many well-studied time lag scheduling problems. The running times of these approximation schemes are polynomial in the number of jobs, but exponential in the num...

Stabilization Criteria for Continuous Linear Time-invariant Systems with Constant Lags

Some criteria for asymptotic stability of linear and time-invariant systems with constant point delays are derived. Such criteria are concerned with the properties of robust stability related to two relevant auxiliary delay-free systems which are built by deleting the delayed dynamics or considering that the delay is zero. Explicit asymptotic stability results, easy to test, are given for both ...

Time Lags: A Feasibility Study

Irreversible Investment, Operating Flexibility, and Time Lags

We consider an optimal investment problem when a firm such as an electric power company has the operational flexibility to expand and contract capacity with fixed cost. This problem is formulated as an impulse control problem combined with optimal stopping. Consequently, we obtain optimal investment timing, optimal capacity expansion and contraction timing, and the investment value. We also sho...