Optimal Dynamic Investment Policy for Different Tax Depreciation Rates and Economic Depreciation Rates

This paper analyzes the investment policy consequences of incorporating a tax depreciation rate different from the economic depreciation rate. Most often, firms choose their tax depreciation rate in a strategic way. Therefore, it would be a coincidence, should the optimization process lead to a tax depreciation rate that equals the economic depreciation rate. The implications of a difference between tax depreciation rate and economic depreciation rate are investigated in an optimal control model for the determination of the firm investment policy over time.     

A breakpoint search approach for convex resource allocation problems with bounded variables

We present an efficient approach to solve resource allocation problems with a single resource, a convex separable objective function, a convex separable resource-usage constraint, and variables that are bounded below and above. Through a combination of function evaluations and median searches, information on whether or not the upper- and lowerbounds are binding is obtained. Once this information is available for all upper and lower bounds, it remains to determine the optimum of a smaller problem with unbounded variables. This can be done through a multiplier search procedure. The information gathered allows for alternative approaches for the multiplier search which can reduce the complexity of this procedure.     

Zebrafish embryo development in a microfluidic flow-through system

The zebrafish embryo is a small, cheap, whole-animal model which may replace rodents in some areas of research. Unfortunately, zebrafish embryos are commonly cultured in microtitre plates using cell-culture protocols with static buffer replacement. Such protocols are highly invasive, consume large quantities of reagents and do not readily permit high-quality imaging. Zebrafish and rodent embryos have previously been cultured in static microfluidic drops, and zebrafish embryos have also been raised in a prototype polydimethylsiloxane setup in a Petri dish. Other than this, no animal embryo has ever been shown to undergo embryonic development in a microfluidic flow-through system. We have developed and prototyped a specialized lab-on-a-chip made from bonded layers of borosilicate glass. We find that zebrafish embryos can develop in the chip for 5 days, with continuous buffer flow at pressures of 0.005-0.04 MPa. Phenotypic effects were seen, but these were scored subjectively as 'minor'. Survival rates of 100% could be reached with buffer flows of 2 μL per well per min. High-quality imaging was possible. An acute ethanol exposure test in the chip replicated the same assay performed in microtitre plates. More than 100 embryos could be cultured in an area, excluding infrastructure, smaller than a credit card. We discuss how biochip technology, coupled with zebrafish larvae, could allow biological research to be conducted in massive, parallel experiments, at high speed and low cost.