A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.

Sleep, metabolism and aging

Aging is a multidimensional process of physical, psychological, and social changes. Understanding how we sleep and how this dynamic process evolves across life span will help to identify normal developmental aspects of sleep over time and to create strategies to increase awareness of sleep disturbances and their early management. In normal sleepers from HypnoLaus cohort, we evaluated the effects of age and gender on both subjective and objective sleep measurements. Our results indicate that normal aging is not accompanied by sleep complaints, and when they exist suggest the presence of underlying comorbidities. Polysomnographic data revealed that slow wave sleep was more affected with age in men, and age affected differently NREM and REM spectral power densities. Both sleep structure and spectral analysis profiles may constitute standards to delineate pathological changes in sleep, both for aging women and men. Another important aspect in the management of sleep and its disorders is a detailed characterization of sleep-inducing medications. Gamma-hydroxybutyrate (GHB) is an inhibitory neurotransmitter derivative of GABA, but its mode of action and the range of effects are not well understood. Several properties, as growth hormone stimulation in humans and the development of weight loss in treated patients suggest an unexplored metabolic effect. In different experiments we assessed the effects of acute, short term and chronic GHB administration on central (cerebral cortex) and peripheral (liver) biochemical processes involved in the metabolism of the drug, as well as the effects of the drug on metabolism in C57BL/6J, GABAB knock-out and obese (ob/ob) mice. We showed that GHB treatment affects weight gain in C57BL/6J and GABAB knock-out mice. Metabolomic analysis indicated large central and peripheral metabolic changes induced by GHB with important relevance to its therapeutic use. -- Le vieillissement est un processus multidimensionnel accompagné par de multiples changements dans les domaines physique, psychologique et social. Comprendre comment nous dormons et comment ce processus dynamique évolue sur la durée de vie nous aidera à identifier les aspects normaux du développement du sommeil au fil du temps, et à créer des stratégies pour accroître la connaissance et compréhension des troubles du sommeil et leur prise en charge précoce. Chez les sujets normaux de la cohorte HypnoLaus nous avons évalué les effets de l'âge et du sexe sur les mesures subjectives et objectives du sommeil. Nos résultats indiquent que le vieillissement normal ne s'accompagne pas de troubles du sommeil, et quand ils existent ceux-ci suggèrent la présence de comorbidités sous-jacentes. Les données polysomnographiques ont révélé que le sommeil profond était plus affecté avec l'âge chez les hommes. De plus, nous avons montré comment l'âge modifie la composition spectrale du sommeil lent et paradoxal. La structure du sommeil et les profils d'analyse spectrale peuvent donc constituer des standards permettant de définir les changements pathologiques du sommeil chez les personnes âgées. Parmi les aspects importants de la gestion du sommeil et de ses troubles, la caractérisation détaillée des médicaments hypnotiques utilisés est essentielle. L'acide gamma-hydroxybutyrique (GHB) est un acide gras à courte chaîne dérivé du GABA, principal neurotransmetteur inhibiteur du cerveau, mais son mode d'action et tous ses effets sont toujours largement méconnus. Plusieurs propriétés, comme la stimulation de la sécrétion de l'hormone de croissance chez l'homme et le développement d'une perte de poids chez les patients traités suggèrent un effet métabolique inexploré. Dans différentes expériences, nous avons évalué les effets d'une exposition aiguë, à court terme et chronique de GHB sur les processus biochimiques centraux (cortex cérébral) et périphériques (foie) impliqués dans le métabolisme du médicament. Nous avons aussi évalué les effets du médicament sur le métabolisme des souris C57BL/6J, GABAB KO et obèses (ob/ob). Nos résultats ont montré que le GHB diminue le gain de poids chez les souris C57BL/6J et GABAB KO. L'analyse métabolomique a indiqué des changements importants induits par GHB au niveau central et périphérique, et ces effets sont importants pour son utilisation thérapeutique.

Riesz-Nágy singular functions revisited

In 1952 F. Riesz and Sz.Nágy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their example was built as the limit of a sequence of deformations of the identity function. As an easy consequence of the definition, the derivative, when it existed and was finite, was found to be zero. In this paper we revisit the Riesz-N´agy family of functions and we relate it to a system for real numberrepresentation which we call (t, t-1) expansions. With the help of these real number expansions we generalize the family. The singularity of the functions is proved through some metrical properties of the expansions used in their definition which also allows us to give a more precise way of determining when the derivative is 0 or infinity.

The use of derivatives in the Spanish mutual fund industry

We study the use of derivatives in the Spanish mutual fund industry. The picture that emerges from our analysis is rather negative. In general, the use of derivatives does not improve the performance of the funds. In only one out of eight categories we find some (very weak and not robust) evidence of superior performance. In most of the cases users significantly underperform non users. Furthermore, users do not seem to exhibit superior timing or selectivity skills either, but rather the contrary. This bad performance is only partially explained by the larger fees funds using derivatives charge. Moreover,we do not find evidence of derivatives being used for hedging purposes. We do find evidence of derivatives being used for speculation. But users in only one category exhibit skills as speculators. Finally, we find evidence of derivatives being used to manage the funds cash inflows and outflows more efficiently.

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.

A note on the Malliavin differentiability of the Heston volatility

We show that the Heston volatility or equivalently the Cox-Ingersoll-Ross process is Malliavin differentiable and give an explicit expression for the derivative. This result assures the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model and the Cox-Ingersoll-Ross model for interest rates.

Carbamazepine augmentation in depressive patients non-responding to citalopram: a pharmacokinetic and clinical pilot study

Citalopram is a chiral antidepressant drug. Its eutomer, S-citalopram (escitalopram), has recently been introduced as an antidepressant. In an open pilot study, four outpatients and two inpatients with a major depressive episode (ICD-10), and who were nonresponders to a 4-week pretreatment with 40-60 mg/day citalopram, were comedicated for another 4-week period with carbamazepine (200-400 mg/day). Some of the patients suffered also from comorbidities: Phobic anxiety disorder with panic attacks (n=2), generalised anxiety disorder, alcohol abuse, dependent personality disorder, hypertension (n=1). After a 4-week augmentation therapy with carbamazepine, a significant (P<0.03) decrease of the plasma concentrations of S-citalopram and R-citalopram, by 27 and 31%, respectively, was observed. Apparently, the probable induction of CYP3A4 by carbamazepine results in a nonstereoselective increase in N-demethylation of citalopram. Moreover, there was a significant (P<0.03) decrease of the ratio S/R-citalopram propionic acid derivative, the formation of it being partly regulated by MAO-A and MAO-B. Already, within 1 week after addition of carbamazepine, there was a slight but significant (P<0.03) decrease of the MADRS depression scores, from 27.0+/-7.7 (mean+/-S.D.) to 23.3+/-6.6, and the final score on day 56 was 18.8+/-10.9. The treatment was generally well tolerated. There was no evidence of occurrence of a serotonin syndrome. After augmentation with carbamazepine, treatment related adverse events were: Nausea in one case, diarrhea in one case, and rash in two cases. In conclusion, the results of this pilot study suggest that carbamazepine augmentation of a citalopram treatment in previous nonresponders to citalopram may be clinically useful, but that in addition carbamazepine can lead to a decrease of the plasma concentrations of the active enantiomer escitalopram.

Persistence and cell culturability of biocontrol strain Pseudomonas fluorescens CHA0 under plough pan conditions in soil and influence of the anaerobic regulator gene anr.

Certain fluorescent pseudomonads can protect plants from soil-borne pathogens, and it is important to understand how these biocontrol agents survive in soil. The persistence of the biocontrol strain Pseudomonas fluorescens CHA0-Rif under plough pan conditions was assessed in non-sterile soil microcosms by counting total cells (immunofluorescence microscopy), intact cells (BacLight membrane permeability test), viable cells (Kogure's substrate-responsiveness test) and culturable cells (colony counts on selective plates) of the inoculant. Viable but non-culturable cells of CHA0-Rif (106 cells g-1 soil) were found in flooded microcosms amended with fermentable organic matter, in which the soil redox potential was low (plough pan conditions), in agreement with previous observations of plough pan samples from a field inoculated with CHA0-Rif. However, viable but non-culturable cells were not found in unamended flooded, amended unflooded or unamended unflooded (i.e. control) microcosms, suggesting that such cells resulted from exposure of CHA0-Rif to a combination of low redox potential and oxygen limitation in soil. CHA0-Rif is strictly aerobic. Its anaerobic regulator ANR is activated by low oxygen concentrations and it controls production of the biocontrol metabolite hydrogen cyanide under microaerophilic conditions. Under plough pan conditions, an anr-deficient mutant of CHA0-Rif and its complemented derivative displayed the same persistence pattern as CHA0-Rif, indicating that anr was not implicated in the formation of viable but non-culturable cells of this strain at the plough pan.

Determination of plasma levels of citalopram and its demethylated and deaminated metabolites by gas chromatography and gas chromatography-mass spectrometry.

Sensitive and specific methods based on gas chromatography (GC) and gas chromatography-mass spectrometry (GC-MS) for the determination of levels of citalopram, desmethylcitalopram and didesmethylcitalopram in the plasma of patients treated with citalopram are presented, as well as a GC-MS procedure for the assay of the citalopram propionic acid derivative. After addition of a separate internal standard for each drug, liquid-solvent extraction is used to separate the basic compounds from the acid compounds. The demethylated amines are derivatized with trifluoroacetic anhydride, and the acid metabolite with methyl iodide. GC-MS is performed in the electron impact mode, as mass spectrometry by the (positive-ion) chemical ionization mode (methane and ammonia) appeared to be unsuitable. The limits of quantification were 1 ng/ml for citalopram and desmethylcitalopram and 2 ng/ml for the other metabolites. The correlation coefficients for the calibration curves (range 10-500 ng/ml) were &gt; or = 0.999 for all compounds, whether determined by GC or GC-MS.

Nitric oxide activity through guanylate cyclase and phosphodiesterase modulation is impaired in fetal lambs with congenital diaphragmatic hernia.

BACKGROUND: Congenital diaphragmatic hernia (CDH) is associated with pulmonary hypertension and death. Administration of nitric oxide (NO) alone remains ineffective in CDH cases. We investigated in near full-term lambs with and without CDH the role of guanylate cyclase (GC), the enzyme activated by NO in increasing cyclic 3'-5'-guanylosine monophosphate, and the role of phosphodiesterase (PDE) 5, the enzyme-degrading cyclic 3'-5'-guanylosine monophosphate. METHODS: Congenital diaphragmatic hernia was surgically created in fetal lambs at 85 days of gestation. Pulmonary hemodynamics were assessed by means of pressure and blood flow catheters (135 days). In vitro, we tested drugs on rings of isolated pulmonary vessels. RESULTS: In vivo, sodium nitroprusside, a direct NO donor, and methyl-2(4-aminophenyl)-1,2-dihydro-1-oxo-7-(2-pyridinylmethoxy)-4-(3,4,5 trimethoxyphenyl)-3-isoquinoline carboxylate sulfate (T-1032) and Zaprinast, both PDE 5 blockers, reduced pulmonary vascular resistance in CDH and non-CDH animals. The activation of GC by sodium nitroprusside and the inhibition of PDE 5 by T-1032 were less effective in CDH animals. In vitro, the stimulation of GC by 3(5'hydroxymethyl-2'furyl)-1-benzyl indazole (YC-1) (a benzyl indazole derivative) and the inhibition of PDE 5 by T-1032 were less effective in pulmonary vascular rings from CDH animals. The YC-1-induced vasodilation in rings from CDH animals was higher when associated with the PDE 5 inhibitor T-1032. CONCLUSIONS: Guanylate cyclase and PDE 5 play a role in controlling pulmonary vascular tone in fetal lambs with or without CDH. Both enzymes seem to be impaired in fetal lambs with CDH.

Igneous garnet and amphibole fractionation in the roots of island arcs: experimental constraints on andesitic liquids

To evaluate the role of garnet and amphibole fractionation at conditions relevant for the crystallization of magmas in the roots of island arcs, a series of experiments were performed on a synthetic andesite at conditions ranging from 0.8 to 1.2 GPa, 800-1,000 degrees C and variable H2O contents. At water undersaturated conditions and fO(2) established around QFM, garnet has a wide stability field. At 1.2 GPa garnet ? amphibole are the high-temperature liquidus phases followed by plagioclase at lower temperature. Clinopyroxene reaches its maximal stability at H2O-contents <= 9 wt% at 950 degrees C and is replaced by amphibole at lower temperature. The slopes of the plagioclase-in boundaries are moderately negative in T-XH2O space. At 0.8 GPa, garnet is stable at magmatic H2O contents exceeding 8 wt% and is replaced by spinel at decreasing dissolved H2O. The liquids formed by crystallization evolve through continuous silica increase from andesite to dacite and rhyolite for the 1.2 GPa series, but show substantial enrichment in FeO/MgO for the 0.8 GPa series related to the contrasting roles of garnet and amphibole in fractionating Fe-Mg in derivative liquids. Our experiments indicate that the stability of igneous garnet increases with increasing dissolved H2O in silicate liquids and is thus likely to affect trace element compositions of H2O-rich derivative arc volcanic rocks by fractionation. Garnet-controlled trace element ratios cannot be used as a proxy

Projecte executiu d'una instal·lació de climatització i control d'un habitatge unifamiliar

Moltes vegades l’usuari d’una instal•lació de climatització o calefacció, no dóna la suficient importància al sistema que l’hi ha de proporcionar un millor confort amb el màxim rendiment. Aquest confort és un factor determinant, entre molts d’altres, de la “qualitat de vida”. Mentre que el rendiment és un factor important a nivell econòmic i ecològic. Tot i tenir prevalença els aspectes d’estalvi energètic, aquests no impliquen haver de renunciar a un confort tèrmic i a un estalvi econòmic. Un dels aspectes que es centra el projecte és promoure l’ús racional de les fonts energètiques (solar, biomassa) per a la correcta climatització dels habitatges. El projecte es desenvolupa en l’àmbit domèstic, concretament correspon a un habitatge unifamiliar. Aquest està situat a la població de Roda de Ter, província de Barcelona. L’objectiu principal del projecte és l’elecció del sistema de climatització i el seu dimensionament, per tal de donar el màxim confort als usuaris que habitin a la vivenda. Criteris ambientals i eficients han estat objecte a considerar pel disseny constructiu de l’habitatge. Una de les mesures importants presses en el projecte, ha estat l’elecció de les diferents parts que formen la instal•lació de climatització. Es fa referència als aïllaments dels tancaments, el sistema solar de recolzament, equips de producció de fred i calor, entre d’altres. En el projecte, s’ha dut a terme un estudi dels diferents tancaments de l’habitatge, tot determinat per a cada un d’ells, el seu coeficient de transmissió tèrmica. Per seleccionar l’equipament més adequat s’ha partit de les condicions climatològiques del municipi de Roda de Ter i s’ha realitzat el càlcul de les necessitats tèrmiques de l’edifici. L’habitatge incorpora una instal•lació de captació solar tèrmica. Aquesta aportarà un suport energètic a tot el sistema de producció de calor, ja sigui per la producció d’aigua calenta sanitària com per el calefactat de la vivenda. La col•locació dels panells a la façana sud tindrà una doble funció: a més de proporcionar energia solar tèrmica, serviran d’elements de protecció solar en la temporada d’estiu. La caldera usada per donar recolzament tèrmic utilitzarà com a combustible el “pellet”. El “pellet” és un tipus de biomassa llenyosa que consta d’un derivat de la fusta en format granulat. Es defineix i es detalla el consum energètic en biomassa, electricitat i cost econòmic anual que ocasionarà la instal.lació dissenyada. El sistema de terra radiant adoptat permetrà el refrescament en èpoques estivals i el calefactat en èpoques hivernals. Aquest donarà el confort tèrmic necessari a cada estança de l’habitatge. En el projecte també es marquen les pautes bàsiques pel control de la instal•lació solar així com el control dels grups de bombament i la mescla d’aigua del terra radiant.

Steady-state equilibrium phase inversion recovery ON-resonant water suppression (IRON) MR angiography in conjunction with superparamagnetic nanoparticles. A robust technique for imaging within a wide range of contrast agent dosages.

PURPOSE: To investigate the ability of inversion recovery ON-resonant water suppression (IRON) in conjunction with P904 (superparamagnetic nanoparticles which consisting of a maghemite core coated with a low-molecular-weight amino-alcohol derivative of glucose) to perform steady-state equilibrium phase MR angiography (MRA) over a wide dose range. MATERIALS AND METHODS: Experiments were approved by the institutional animal care committee. Rabbits (n = 12) were imaged at baseline and serially after the administration of 10 incremental dosages of 0.57-5.7 mgFe/Kg P904. Conventional T1-weighted and IRON MRA were obtained on a clinical 1.5 Tesla (T) scanner to image the thoracic and abdominal aorta, and peripheral vessels. Contrast-to-noise ratios (CNR) and vessel sharpness were quantified. RESULTS: Using IRON MRA, CNR and vessel sharpness progressively increased with incremental dosages of the contrast agent P904, exhibiting constantly higher contrast values than T1 -weighted MRA over a very wide range of contrast agent doses (CNR of 18.8 ± 5.6 for IRON versus 11.1 ± 2.8 for T1 -weighted MRA at 1.71 mgFe/kg, P = 0.02 and 19.8 ± 5.9 for IRON versus -0.8 ± 1.4 for T1-weighted MRA at 3.99 mgFe/kg, P = 0.0002). Similar results were obtained for vessel sharpness in peripheral vessels, (Vessel sharpness of 46.76 ± 6.48% for IRON versus 33.20 ± 3.53% for T1-weighted MRA at 1.71 mgFe/Kg, P = 0.002, and of 48.66 ± 5.50% for IRON versus 19.00 ± 7.41% for T1-weighted MRA at 3.99 mgFe/Kg, P = 0.003). CONCLUSION: Our study suggests that quantitative CNR and vessel sharpness after the injection of P904 are consistently higher for IRON MRA when compared with conventional T1-weighted MRA. These findings apply for a wide range of contrast agent dosages.

Combined Electrostatic and Covalent Polymer Networks for Cell Microencapsulation

Two types of hydrogel microspheres have been developed. Fast ionotropic gelation of sodium alginate (Na-alg) in the presence of calcium ions was combined with slow covalent cross-linking of poly(ethylene glycol) (PEG) derivatives. For the first type, the fast obtainable Ca-alg hydrogel served as spherical matrix for the simultaneously occurring covalent cross-linking of multi-arm PEG derivative. A two-component interpenetrating network was formed in one step upon extruding the mixture of the two polymers into the gelation bath. For the second type, heterobifunctional PEG was grafted onto Na-alg prior to gelation. Upon extrusion of the polymer solution into the gelation bath, fast Ca-alg formation ensured the spherical shape and was accompanied by cross-linker-free covalent cross-linking of the PEG side chains. Thus, one-component hydrogel microspheres resulted. We present the physical properties of the hydrogel microspheres and demonstrate the feasibility of cell microencapsulation for both types of polymer networks.