On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.Black-Scholes formula, derivative operator, Itô's formula for the Skorohod integral, jump-diffusion stochastic volatility model

Characterizing steady states of genome-scale metabolic networks in continuous cell cultures

We present a model for continuous cell culture coupling intra-cellular metabolism to extracellular variables describing the state of the bioreactor, taking into account the growth capacity of the cell and the impact of toxic byproduct accumulation. We provide a method to determine the steady states of this system that is tractable for metabolic networks of arbitrary complexity. We demonstrate our approach in a toy model first, and then in a genome-scale metabolic network of the Chinese hamster ovary cell line, obtaining results that are in qualitative agreement with experimental observations. More importantly, we derive a number of consequences from the model that are independent of parameter values. First, that the ratio between cell density and dilution rate is an ideal control parameter to fix a steady state with desired metabolic properties invariant across perfusion systems. This conclusion is robust even in the presence of multi-stability, which is explained in our model by the negative feedback loop on cell growth due to toxic byproduct accumulation. Moreover, a complex landscape of steady states in continuous cell culture emerges from our simulations, including multiple metabolic switches, which also explain why cell-line and media benchmarks carried out in batch culture cannot be extrapolated to perfusion. On the other hand, we predict invariance laws between continuous cell cultures with different parameters. A practical consequence is that the chemostat is an ideal experimental model for large-scale high-density perfusion cultures, where the complex landscape of metabolic transitions is faithfully reproduced. Thus, in order to actually reflect the expected behavior in perfusion, performance benchmarks of cell-lines and culture media should be carried out in a chemostat

El reconocimiento de la hidalguía durante el siglo XVIII: su reformulación como calidad civil y política

Throughout The Modern Age the hidalguía suffered a serious conceptual evolution. At the end of the Ancien Régime the loss of the medieval features and its conversion to a legal reality regulated by the State were one of the most prominent characteristics. In this research we analyze the transformational factors of the nobility in a legal statute closely regulated which was at the service of the absolutist monarchy. In order to analyze it we have chosen processes of hidalguía initiated in the Royal Chancelleries as the core idea of the research, demonstrating that, their utility was not only as instruments used to supervise the access to nobility, but, what is more, they are a form of the new identity adopted by the Bourbon nobility; the subordinate state which depends on the crown.A lo largo de la Edad Moderna la hidalguía experimentaría una significativa evolución conceptual. A finales del Antiguo Régimen, la pérdida de sus rasgos medievales y su conversión en una realidad jurídica regulada por el Estado serían algunas de sus características más destacadas. En este trabajo analizaremos los factores de la transformación de la hidalguía en un estatuto jurídico estrechamente fiscalizado y al servicio de la monarquía absolutista. Para ello, hemos elegido como eje de la investigación los procesos de hidalguía incoados ante las Reales Chancillerías que, como aquí demostraremos, no solo sirvieron como instrumentos para supervisar el acceso a la hidalguía sino que además son una plasmación de la nueva identidad adoptada por la nobleza borbónica: la de un estamento subordinado y dependiente de la Corona