Delayed decision-making in bistable models

Switching between two modes of operation is a common property of biological systems. In continuous-time differential equation models, this is often realised by bistability, i.e. the existence of two asymptotically stable steadystates. Several biological models are shown to exhibit delayed switching, with a pronounced transient phase, in particular for near-threshold perturbations. This study shows that this delay in switching from one mode to the other in response to a transient input is reflected in local properties of an unstable saddle point, which has a one dimensional unstable manifold with a significantly slower eigenvalue than the stable ones. Thus, the trajectories first approximatively converge to the saddle point, then linger along the saddle's unstable manifold before quickly approaching one of the stable equilibria. ©2010 IEEE.

Delayed control of a Moore-Greitzer axial compressor model

Several feedback control laws have appeared in the literature concerning the stabilization of the nonlinear Moore-Greitzer axial compression model. Motivated by magnitude and rate limitations imposed by the physical implementation of the control law, Larsen et al. studied a dynamic implementation of the S-controller suggested by Sepulchre and Kokotović. They showed the potential benefit of implementing the S-controller through a first-order lag: while the location of the closed-loop equilibrium achieved with the static control law was sensitive to poorly known parameters, the dynamic implementation resulted in a small limit cycle at a very desirable location, insensitive to parameter variations. In this paper, we investigate the more general case when the control is applied with a time delay. This can be seen as an extension of the model with a first-order lag. The delay can either be a result of system constraints or be deliberately implemented to achieve better system behavior. The resulting closed-loop system is a set of parameter-dependent delay differential equations. Numerical bifurcation analysis is used to study this model and investigate whether the positive results obtained for the first-order model persist, even for larger values of the delay.

Tests of an adaptive QM/MM calculation on free energy profiles of chemical reactions in solution.

We present reaction free energy calculations using the adaptive buffered force mixing quantum mechanics/molecular mechanics (bf-QM/MM) method. The bf-QM/MM method combines nonadaptive electrostatic embedding QM/MM calculations with extended and reduced QM regions to calculate accurate forces on all atoms, which can be used in free energy calculation methods that require only the forces and not the energy. We calculate the free energy profiles of two reactions in aqueous solution: the nucleophilic substitution reaction of methyl chloride with a chloride anion and the deprotonation reaction of the tyrosine side chain. We validate the bf-QM/MM method against a full QM simulation, and show that it correctly reproduces both geometrical properties and free energy profiles of the QM model, while the electrostatic embedding QM/MM method using a static QM region comprising only the solute is unable to do so. The bf-QM/MM method is not explicitly dependent on the details of the QM and MM methods, so long as it is possible to compute QM forces in a small region and MM forces in the rest of the system, as in a conventional QM/MM calculation. It is simple, with only a few parameters needed to control the QM calculation sizes, and allows (but does not require) a varying and adapting QM region which is necessary for simulating solutions.

Characterization of light and heavy hydrated magnesium carbonates using thermal analysis

Upon heating, hydrated magnesium carbonates (HMCs) undergo a continuous sequence of decomposition reactions. This study aims to investigate the thermal decomposition of various commercially produced HMCs classified as light and heavy, highlight their differences, and provide an insight into their compositions in accordance with the results obtained from thermal analysis and microstructure studies. An understanding of the chemical compositions and microstructures, and a better knowledge of the reactions that take place during the decomposition of HMCs were achieved through the use of SEM, XRD, and TG/differential thermal analysis (DTA). The quantification of their CO 2 contents was provided by TG and dissolving the samples in HCl acid. Results show that variations exist within the microstructure and decomposition patterns of the two groups of HMCs, which do not exactly fit into the fixed stoichiometry of the known HMCs in the MgO-CO2-H2O system. The occurrence of an exothermic DTA peak was only observed for the heavy HMCs, which was attributed to their high CO2 contents and the relatively delayed decomposition pattern. © 2013 Akadémiai Kiadó, Budapest, Hungary.

Delayed-decision making in noisy bistable switches

Bistable switches are frequently encountered in biological systems. Typically, a bistable switch models a binary decision where each decision corresponds to one of the two stable equilibria. Recently, we showed that the global decision-making process in bistable switches strongly depends on a particular equilibrium point of these systems, their saddle point. In particular, we showed that a saddle point with a time-scale separation between its attractive and repulsive directions can delay the decision-making process. In this paper, we study the effects of white Gaussian noise on this mechanism of delayed decision-making induced by the saddle point. Results show that the mean decision-time strongly depends on the balance between the initial distance to the separatrix and the noise strength. © IFAC.