A semi-nonparametric generalized multinomial logit model, formulated using orthonormal Legendre polynomials to extend the standard Gumbel distribution, is presented in this paper. The resulting semi-nonparametric function can represent a probability density function for a large family of multimodal distributions. The model has a closed-form log-likelihood function that facilitates model estimation. The proposed method is applied to model commute mode choice among four alternatives (auto, transit, bicycle and walk) using travel behavior data from Argau, Switzerland. Comparisons between the multinomial logit model and the proposed semi-nonparametric model show that violations of the standard Gumbel distribution assumption lead to considerable inconsistency in parameter estimates and model inferences.

The production, characterization, and antioxidant capacity of the carotenoid fucoxanthin from the marine diatom Odontella aurita were investigated. The results showed that low light and nitrogen-replete culture medium enhanced the biosynthesis of fucoxanthin. The maximum biomass concentration of 6.36 g L^-1 and maximum fucoxanthin concentration of 18.47 mg g^-1 were obtained in cultures grown in a bubble column photobioreactor (Ø 3.0 cm inner diameter), resulting in a fucoxanthin volumetric productivity of 7.96 mg L^-1 day^-1. A slight reduction in biomass production was observed in the scaling up of O. aurita culture in a flat plate photobioreactor, yet yielded a comparable fucoxanthin volumetric productivity. A rapid method was developed for extraction and purification of fucoxanthin. The purified fucoxanthin was identified as all-trans-fucoxanthin, which exhibited strong antioxidant properties, with the effective concentration for 50% scavenging (EC₅₀) of 1,1-dihpenyl-2-picrylhydrazyl (DPPH) radical and 2,2′-Azino-bis(3-ethylbenzthiazoline-6-sulfonic acid (ABTS) radical being 0.14 and 0.03 mg mL^-1, respectively. Our results suggested that O. aurita can be a natural source of fucoxanthin for human health and nutrition.