Developmental dynamics of multicellular organism is a process that takes place in a multi-stable system in which each attractor state represents a cell type and attractor transitions correspond to cell differentiation paths. This new understanding has revived the idea of a quasi-potential landscape, first proposed by Waddington as a metaphor. To describe development one is interested in the "relative stabilities" of N attractors (N>2). Existing theories of state transition between local minima on some potential landscape deal with the exit in the transition between a pair attractor but do not offer the notion of a global potential function that relate more than two attractors to each other. Several ad hoc methods have been used in systems biology to compute a landscape in non-gradient systems, such as gene regulatory networks. Here we present an overview of the currently available methods, discuss their limitations and propose a new decomposition of vector fields that permit the computation of a quasi-potential function that is equivalent to the Freidlin-Wentzell potential but is not limited to two attractors. Several examples of decomposition are given and the significance of such a quasi-potential function is discussed.

Quasi-potential landscape in complex multi-stable systems

Optimisation of Thermal Processing - A Review

Modeling of chemical reactors — XVI Steady state axial heat and mass transfer in tubular reactors An analysis of the uniqueness of solutions

The maximum principle theory (Pontryagin et al., 1962) was used to optimize thiamin retention during sterilization of a conduction-heating canned food. The optimal retort temperature Profile determined by this procedure improved thiamin retention by more than 2%, as Compared with other methods, and showed that a single solution for the temperature profile exists. This optimization method may be applicable to other processes in which retention of nutrients or other characteristics is to be improved.

E.S. Lee

Papers

Quasi-linearization, non-linear boundary value problems and optimization

A generalized Newton-Raphson method for nonlinear partial differential equations—packed-bed reactors with axial mixing