Brief note on the variation of constants formula for fuzzy differential equations

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue-eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution. (C) 2002 Elsevier Science B.V. All rights reserved.

A simple formula for the average gate fidelity of a quantum dynamical operation

This Letter presents a simple formula for the average fidelity between a unitary quantum gate and a general quantum operation on a qudit, generalizing the formula for qubits found by Bowdrey et al. [Phys. Lett. A 294 (2002) 258]. This formula may be useful for experimental determination of average gate fidelity. We also give a simplified proof of a formula due to Horodecki et al. [Phys. Rev. A 60 (1999) 1888], connecting average gate fidelity to entanglement fidelity. (C) 2002 Elsevier Science B.V. All rights reserved.

Novel foods across the lifespan: From infant formula to impact on ageing

The purpose of the present paper was to examine the scope of novel foods in improving and/or preventing the nutritional disorders in different stages of lifespan. First, attempts were made to review the current trend and magnitude of the nutritional problems in each of the stages starting from fetal development to old age. The paper then describes the possible potential role of novel foods in alleviating and/or preventing these nutritional/health problems. The conclusion made is that the novel foods have a great potential for improving the overall nutritional status throughout the lifespan, thereby reducing the risk of early death or disability due to chronic diseases. However, to achieve a noticeable impact of novel foods on public health, efforts are needed to ensure that these foods are available and affordable to the population most at risk.