Productivity estimated as in vivo chlorophyll a fluorescence and biochemical composition in Chlorella fusca (Chlorophyta) grown in outdoor thin-layer cascades

The photosynthetic performance by using in vivo chlorophyll a florescence, biomass composition and productivity of three cultures of Chlorella fusca (Chlorophyta) grown in thin-layer cascades (TLCs) in different locations and time of the year were evaluated. Biomass productivity was higher in 120 m-1 S/V TLC (3.65 g L-1 d-1) compared at 27 m-1 S/V TLC (0.08-0.15 g L-1 d-1). Online monitoring of in vivo chlorophyll fluorescence provided data with high temporal resolution. The simultaneous measure of the PAR irradiance and the effective quantum yield together to the determination of absorption coefficient allowed the determination of daily Electron transport rate (ETR), what led to the estimation of biomass productivity by using conversion factors of mol photons per oxygen produced and relation between carbon assimilated and oxygen produced. The relation between estimated productivity and measured productivity estimated as g l-1 d-1 was 0.90 with R2=0.94. Final biochemical composition was similar in summer culture independent of the S/V of the TLC i.e 30-37% DW lipids, 30-34 % DW proteins and 16-19% DW starch. Lower accumulation was found in autumn cultures, ~23, 28% and 13% DW for lipid and starch content, respectively. The S/V ratio of the system was a key factor to obtain high biomass and storage product productivity. This strain was able to grow outdoors in TLC, exhibiting very high productivity according to the optimal photosynthetic performance and accumulating high lipid and protein content. It is shown as first time a good estimation of algal biomass productivity by using daily integrated values of electron transport rate (ETR) converted to estimated biomass productivity.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Sieve-based confidence intervals and bands for L\'{e}vy densities

The estimation of the L\'{e}vy density, the infinite-dimensional parameter controlling the jump dynamics of a L\'{e}vy process, is considered here under a discrete-sampling scheme. In this setting, the jumps are latent variables, the statistical properties of which can be assessed when the frequency and time horizon of observations increase to infinity at suitable rates. Nonparametric estimators for the L\'{e}vy density based on Grenander's method of sieves was proposed in Figueroa-L\'{o}pez [IMS Lecture Notes 57 (2009) 117--146]. In this paper, central limit theorems for these sieve estimators, both pointwise and uniform on an interval away from the origin, are obtained, leading to pointwise confidence intervals and bands for the L\'{e}vy density. In the pointwise case, our estimators converge to the L\'{e}vy density at a rate that is arbitrarily close to the rate of the minimax risk of estimation on smooth L\'{e}vy densities. In the case of uniform bands and discrete regular sampling, our results are consistent with the case of density estimation, achieving a rate of order arbitrarily close to $\log^{-1/2}(n)\cdot n^{-1/3}$, where $n$ is the number of observations. The convergence rates are valid, provided that $s$ is smooth enough and that the time horizon $T_n$ and the dimension of the sieve are appropriately chosen in terms of $n$.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ286 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Existence of minimal and maximal solutions to first--order differential equations with state--dependent deviated arguments

We prove some new results on existence of solutions to first--order ordinary differential equations with deviating arguments. Delay differential equations are included in our general framework, which even allows deviations to depend on the unknown solutions. Our existence results lean on new definitions of lower and upper solutions introduced in this paper, and we show with an example that similar results with the classical definitions are false. We also introduce an example showing that the problems considered need not have the least (or the greatest) solution between given lower and upper solutions, but we can prove that they do have minimal and maximal solutions in the usual set--theoretic sense. Sufficient conditions for the existence of lower and upper solutions, with some examples of application, are provided too

Small-time asymptotics of stopped L\'evy bridges and simulation schemes with controlled bias

We characterize the small-time asymptotic behavior of the exit probability of a L\'evy process out of a two-sided interval and of the law of its overshoot, conditionally on the terminal value of the process. The asymptotic expansions are given in the form of a first-order term and a precise computable error bound. As an important application of these formulas, we develop a novel adaptive discretization scheme for the Monte Carlo computation of functionals of killed L\'evy processes with controlled bias. The considered functionals appear in several domains of mathematical finance (e.g., structural credit risk models, pricing of barrier options, and contingent convertible bonds) as well as in natural sciences. The proposed algorithm works by adding discretization points sampled from the L\'evy bridge density to the skeleton of the process until the overall error for a given trajectory becomes smaller than the maximum tolerance given by the user.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ517 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm