Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Background: Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results: Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions: Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Data-division-specific robustness and power of randomization tests for ABAB designs

This study deals with the statistical properties of a randomization test applied to an ABAB design in cases where the desirable random assignment of the points of change in phase is not possible. In order to obtain information about each possible data division we carried out a conditional Monte Carlo simulation with 100,000 samples for each systematically chosen triplet. Robustness and power are studied under several experimental conditions: different autocorrelation levels and different effect sizes, as well as different phase lengths determined by the points of change. Type I error rates were distorted by the presence of autocorrelation for the majority of data divisions. Satisfactory Type II error rates were obtained only for large treatment effects. The relationship between the lengths of the four phases appeared to be an important factor for the robustness and the power of the randomization test.

Improving the efficiency of PV low-power processing circuits by selecting an optimal inductor current of the DC/DC converter

In the context of autonomous sensors powered by small-size photovoltaic (PV) panels, this work analyses how the efficiency of DC/DC-converter-based power processing circuits can be improved by an appropriate selection of the inductor current that transfers the energy from the PV panel to a storage unit. Each component of power losses (fixed, conduction and switching losses) involved in the DC/DC converter specifically depends on the average inductor current so that there is an optimal value of this current that causes minimal losses and, hence, maximum efficiency. Such an idea has been tested experimentally using two commercial DC/DC converters whose average inductor current is adjustable. Experimental results show that the efficiency can be improved up to 12% by selecting an optimal value of that current, which is around 300-350 mA for such DC/DC converters.

The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements

A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement, which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with the findings in the literature and with physical and SPICE models, the equilateral triangular power pad arrangement is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.