On a family of rational perturbations of the doubling map

The goal of this paper is to investigate the parameter plane of a rational family of perturbations of the doubling map given by the Blaschke products $B_a(z)=z^3\frac{z-a}{1-\bar{a}z}$. First we study the basic properties of these maps such as the connectivity of the Julia set as a function of the parameter $a$. We use techniques of quasiconformal surgery to explore the relation between certain members of the family and the degree 4 polynomials $\left(\overline{\overline{z}^2+c}\right)^2+c$. In parameter space, we classify the different hyperbolic components according to the critical orbits and we show how to parametrize those of disjoint type

Dynamical mechanism behind ghosts unveiled in a map complexification

Complex systems such as ecosystems, electronic circuits, lasers, or chemical reactions can be modelled by dynamical systems which typically experience bifurcations. It is known that transients become extremely long close to bifurcations, also following well-defined scaling laws as the bifurcation parameter gets closer the bifurcation value. For saddle-node bifurcations, the dynamical mechanism responsible for these delays, tangible at the real numbers phase space (so-called ghosts), occurs at the complex phase space. To study this phenomenon we have complexified an ecological map with a saddle-node bifurcation. We have investigated the complex (as opposed to real) dynamics after this bifurcation, identifying the fundamental mechanism causing such long delays, given by the presence of two repellers in the complex space. Such repellers appear to be extremely close to the real line, thus forming a narrow channel close to the two new fixed points and responsible for the slow passage of the orbits. We analytically provide the relation between the well-known inverse square-root scaling law of transient times and the multipliers of these repellers. We finally prove that the same phenomenon occurs for more general i.e. non-necessarily polynomial, models

Inferència Estadística Aplicada

Aquest llibre conté els temes fonamentals dels models de probabilitat i d’inferència estadística. Per al seu seguiment no és necessari cap coneixement previ d’aquestes matèries però se suposa que el lector està familiaritzat amb l’estadística descriptiva. S’han dedicat els dos últims capítols a tècniques estadístiques aplicades a l’economia: model de regressió, nombre índex i sèries temporals. El llibre s’orienta cap a les aplicacions pràctiques, així cada nou concepte i mètode s’il·lustra amb exemples oferint al lector una comprensió intuïtiva del concepte. L’obra s’adreça a tota persona interessada en aplicar les tècniques d’inferència estadística especialment als àmbits econòmic, empresarial i social

Biocatalytic Transformation of 5-Hydroxymethylfurfural into 2,5-di(hydroxymethyl)furan by a Newly Isolated Fusarium striatum Strain

The compound 2,5-di(hydroxymethyl)furan (DHMF) is a high-value chemical block that can be synthesized from 5-hydroxymethylfurfural (HMF), a platform chemical that results from the dehydration of biomass-derived carbohydrates. In this work, the HMF biotransformation capability of different Fusarium species was evaluated, and F. striatum was selected to produce DHMF. The effects of the inoculum size, glucose concentration and pH of the media over DHMF production were evaluated by a 23 factorial design. A substrate feeding approach was found suitable to overcome the toxicity effect of HMF towards the cells when added at high concentrations (>75 mM). The process was successfully scaled-up at bioreactor scale (1.3 L working volume) with excellent DHMF production yields (95%) and selectivity (98%). DHMF was purified from the reaction media with high recovery and purity by organic solvent extraction with ethyl acetate.This work was partially supported by the Spanish government (PID2019-110735RB-C21, MICIN/FEDER) and the Catalan Government (FI_B1_00135)

Tongues in degree 4 Blaschke products

The goal of this paper is to investigate the family of Blasche products B_a , which is a rational family of perturbations of the doubling map. We focus on the tongue-like sets which appear in its parameter plane. We first study their basic topological properties and afterwards we investigate how bifurcations take place in a neighborhood of their tips. Finally we see how the fixed tongue extends beyond its natural domain of definition

Preparation of (S)-1-halo-2-octanols using ionic liquids and biocatalysts

Preparation of (S)-1-chloro-2-octanol and (S)-1-bromo-2-octanol was carried out by the enzymatic hydrolysis of halohydrin palmitates using biocatalysts. Halohydrin palmitates were prepared by various methods from palmitic acid and 1,2-octanediol. A tandem hydrolysis was carried out using lipases from Candida antarctica (Novozym® 435), Rhizomucor miehei (Lipozyme IM), and “resting cells” from a Rhizopus oryzae strain that was not mycotoxigenic. The influence of the enzyme and the reaction medium on the selective hydrolysis of isomeric mixtures of halohydrin esters is described. Novozym® 435 allowed preparation of (S)-1-chloro-2-octanol and (S)-1-bromo-2-octanol after 1–3 h ofreaction at 40 °C in [BMIM][PF6]

The transcriptional co-activator PCAF regulates cdk2 activity

Cyclin dependent kinases (cdks) regulate cell cycle progression and transcription. We report here that the transcriptional co-activator PCAF directly interacts with cdk2. This interaction is mainly produced during S and G2/M phases of the cell cycle. As a consequence of this association, PCAF inhibits the activity of cyclin/cdk2 complexes. This effect is specific for cdk2 because PCAF does not inhibit either cyclin D3/cdk6 or cyclin B/cdk1 activities. The inhibition is neither competitive with ATP, nor with the substrate histone H1 suggesting that somehow PCAF disturbs cyclin/cdk2 complexes. We also demonstrate that overexpression of PCAF in the cells inhibits cdk2 activity and arrests cell cycle progression at S and G2/M. This blockade is dependent on cdk2 because it is rescued by the simultaneous overexpression of this kinase. Moreover, we also observed that PCAF acetylates cdk2 at lysine 33. As this lysine is essential for the interaction with ATP, acetylation of this residue inhibits cdk2 activity. Thus, we report here that PCAF inhibits cyclin/cdk2 activity by two different mechanisms: (i) by somehow affecting cyclin/cdk2 interaction and (ii) by acetylating K33 at the catalytic pocket of cdk2. These findings identify a previously unknown mechanism that regulates cdk2 activity