On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

HSU-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.

Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

Hours worked - Productivity puzzle: identification in fractional integration settings

A recent finding of the structural VAR literature is that the response of hours worked to a technology shock depends on the assumption on the order of integration of the hours. In this work we relax this assumption, allowing for fractional integration and long memory in the process for hours and productivity. We find that the sign and magnitude of the estimated impulse responses of hours to a positive technology shock depend crucially on the assumptions applied to identify them. Responses estimated with short-run identification are positive and statistically significant in all datasets analyzed. Long-run identification results in negative often not statistically significant responses. We check validity of these assumptions with the Sims (1989) procedure, concluding that both types of assumptions are appropriate to recover the impulse responses of hours in a fractionally integrated VAR. However, the application of longrun identification results in a substantial increase of the sampling uncertainty. JEL Classification numbers: C22, E32. Keywords: technology shock, fractional integration, hours worked, structural VAR, identification

Synthesis, binding affinity, and molecular docking analysis of new benzofuranone derivative as pontential antipsychotics

The complex etiology of schizophrenia has prompted researchers to develop clozapine-related multitargetstrategies to combat its symptoms. Here we describe a series of new 6-aminomethylbenzofuranones in aneffort to find new chemical structures with balanced affinities for 5-HT2 and dopamine receptors. Throughbiological and computational studies of 5-HT2A and D2 receptors, we identified the receptor serine residuesS3.36 and S5.46 as the molecular keys to explaining the differences in affinity and selectivity betweenthese new compounds for this group of receptors. Specifically, the ability of these compounds to establishone or two H-bonds with these key residues appears to explain their difference in affinity. In addition, wedescribe compound 2 (QF1004B) as a tool to elucidate the role of 5-HT2C receptors in mediating antipsychoticeffects and metabolic adverse events. The compound 16a (QF1018B) showed moderate to high affinitiesfor D2 and 5-HT2A receptors, and a 5-HT2A/D2 ratio was predictive of an atypical antipsychotic profile.

A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatilityframework can be decomposed in the sum of four terms, which identifythe main features of the market that affect to option prices: the expectedfuture volatility, the correlation between the volatility and the noisedriving the stock prices, the market price of volatility risk and thedifference of the expected future volatility at different times. We alsostudy some applications of this decomposition.

Is the observed persistence spurious? A test for fractional integration versus short memory and structural breaks

Although it is commonly accepted that most macroeconomic variables are nonstationary, it is often difficult to identify the source of the non-stationarity. In particular, it is well-known that integrated and short memory models containing trending components that may display sudden changes in their parameters share some statistical properties that make their identification a hard task. The goal of this paper is to extend the classical testing framework for I(1) versus I(0)+ breaks by considering a a more general class of models under the null hypothesis: non-stationary fractionally integrated (FI) processes. A similar identification problem holds in this broader setting which is shown to be a relevant issue from both a statistical and an economic perspective. The proposed test is developed in the time domain and is very simple to compute. The asymptotic properties of the new technique are derived and it is shown by simulation that it is very well-behaved in finite samples. To illustrate the usefulness of the proposed technique, an application using inflation data is also provided.

Differential equations driven by fractional Brownian motion

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H> is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

Assessment of the potential skin irritation of lysine-derivative anionic surfactants using mouse fibroblast and human keratinocytes as an alternative to animal testing

Purpose. The aim of this study was to identify new surfactants with low skin irritant properties for use in pharmaceutical and cosmetic formulations, employing cell culture as an alternative method to in vivo testing. In addition, we sought to establish whether potential cytotoxic properties were related to the size of the counterions bound to the surfactants. Methods. Cytotoxicity was assessed in the mouse fibroblast cell line 3T6, and the human keratinocyte cell line NCTC 2544, using the MTT assay and uptake of the vital dye neutral red 24 h after dosing (NRU). Results. Lysine-derivative surfactants showed higher IC50s than did commercial anionic irritant compounds such as sodium dodecyl sulphate, proving to be no more harmful than amphoteric betaines. The aggressiveness of the surfactants depended upon the size of their constituent counterions: surfactants associated with lighter counterions showed a proportionally higher aggressivity than those with heavier ones. Conclusions. Synthetic lysine-derivative anionic surfactants are less irritant than commercial surfactants such as sodium dodecyl sulphate and Hexadecyltrimethylammonium bromide and are similar to Betaines. These surfactants may offer promising applications in pharmaceutical and cosmetic preparations, representing a potential alternative to commercial anionic surfactants as a result of their low irritancy potential.

Power variation of some integral fractional processes

We consider the asymptotic behaviour of the realized power variation of processes of the form ¿t0usdBHs, where BH is a fractional Brownian motion with Hurst parameter H E(0,1), and u is a process with finite q-variation, q<1/(1¿H). We establish the stable convergence of the corresponding fluctuations. These results provide new statistical tools to study and detect the long-memory effect and the Hurst parameter.

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Development of an epidermal growth factor derivative with EGFR blocking activity.

The members of the epidermal growth factor (EGF)/ErbB family are prime targets for cancer therapy. However, the therapeutic efficiency of the existing anti-ErbB agents is limited. Thus, identifying new molecules that inactivate the ErbB receptors through novel strategies is an important goal on cancer research. In this study we have developed a shorter form of human EGF (EGFt) with a truncated C-terminal as a novel EGFR inhibitor. EGFt was designed based on the superimposition of the three-dimensional structures of EGF and the Potato Carboxypeptidase Inhibitor (PCI), an EGFR blocker previously described by our group. The peptide was produced in E. coli with a high yield of the correctly folded peptide. EGFt showed specificity and high affinity for EGFR but induced poor EGFR homodimerization and phosphorylation. Interestingly, EGFt promoted EGFR internalization and translocation to the cell nucleus although it did not stimulate the cell growth. In addition, EGFt competed with EGFR native ligands, inhibiting the proliferation of cancer cells. These data indicate that EGFt may be a potential EGFR blocker for cancer therapy. In addition, the lack of EGFR-mediated growth-stimulatory activity makes EGFt an excellent delivery agent to target toxins to tumours over-expressing EGFR.