Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times

We apply previous results on the pathwise exponential loss of memory of the initial condition for stochastic differential equations with small diffusion to the problem of the asymptotic distribution of the first exit times from an attracted domain. We show under general hypotheses that the suitably rescaled exit time converges in the zero-noise limit to an exponential random variable. Then we extend the results to an infinite-dimensional case obtained by adding a small random perturbation to a nonlinear heat equation.     

Triorganotin 4-isopropylbenzoates as model transesterification catalysts for triorganotin carboxylates grafted to cross-linked polystyrene

Starting from 4-isopropylbenzoic acid, three new triorganotin carboxylates bearing methyl, butyl and phenyl substituents at tin, respectively, were prepared and fully characterized by spectroscopic and thermal techniques, with particular regard to the coordination number of tin atom, in solution as well as in the solid state. The triorganotin compounds, tested as transesterification catalysts in the reaction between ethyl acetate and primary, secondary or tertiary alcohol, respectively, displayed, as expected, a strong decrease of activity on passing from the primary to the tertiary alcohol reactant. Different activities by the tin carboxylates were also observed in the reaction between primary alcohol and ethyl acetate. The reaction mechanism, as elucidated by Sn NMR, involves coordination of both ester substrate and alcohol reactant to the triorganotin compound, the reaction conversion appearing related not only to the Lewis acidity of the tin atom, but also to the nature of the reactants. Preliminary catalytic tests were also carried out in the reaction between glyceryl tridodecanoate (as a model of natural triglyceride) and ethanol, mimicking the preparation of biodiesel fuel. Although in this case lower conversions were obtained with respect to the reactions on ethyl acetate, the catalytic activity of organotin derivatives appears considerable.     

PHEMA hydrogels obtained by a novel low-heat curing procedure with a potential for in situ preparation

In this work, we report on poly(2-hydroxyethyl methacrylate) (PHEMA) hydrogels obtained by a low heat curing reaction. These materials are suitable for in situ preparation and therefore endowed with a potential for several biomedical applications. The novel procedure adopted involves as the first step the synthesis of a soluble oligomeric PHEMA precursor containing polymerizable functions as side substituents. As the second step, the precursor is dissolved in equal amounts of 2-hydroxyethyl methacrylate (HEMA) and water, to form a viscous but still injectable syrup. A low temperature water soluble initiator is then added. The curing reaction starts promptly and is completed within few minutes. During the entire process the internal temperature never rises above 40 degrees C. Preliminary mechanical characterizations performed on the hydrogels in their water-swollen state and diffusion tests in absorption/desorption experiments clearly indicated that on all respects the novel hydrogels are comparable with conventional PHEMA hydrogels obtained according to literature from HEMA in the presence of divinyl crosslinkers. However, the much shorter curing time combined with the far lower curing temperature endow the new hydrogels with a higher potential in view of specific surgical requirements, and particularly for in situ preparation.     

Positive and negative ion chemistry of the anesthetic halothane (1-bromo-1-chloro-2,2,2-trifluoroethane) in air plasma at atmospheric pressure

The ion chemistry of 1-bromo-1-chloro-2,2,2-trifluoroethane (the common anesthetic halothane) in air plasma at atmospheric pressure was investigated by atmospheric pressure chemical ionization mass spectrometry (APCI-MS). The major positive ion observed at low declustering (API interface) energies is the ionized dimer, M(+.)M, an unexpectedly abundant species which possibly is stabilized by two H-bonding interactions. At higher energies [M--HF](+.) and [M--Br](+) prevail; the former, corresponding to ionized olefin [ClBrC=CF(2)](+.), appears to originate from M(+.)M and is quite stable towards fragmentation. The latter fragment ion ([M--Br](+)) and its analogue, [M--Cl](+), which is also observed though at much lower abundance, are originally ethyl cations (+)CHX--CF(3) (X = Br, Cl) which, upon collisional activation, rearrange and fragment to CHFX(+) via elimination of CF(2). All of the above described ions are also observed in humid air: in addition, the oxygenated ion [ClBrC=CFOH](+.) also forms in humid air via water addition to [ClBrC=CF(2)](+.) and HF elimination, as observed earlier for ionized trichloroethene. In contrast with similar chloro- and fluoro-substituted ethanes, halothane does not react with H(3)O(+) in the APCI plasma, a result confirmed by selected ion APCI triple-quadrupole (TQ) experiments. Major negative ions formed from halothane in the air plasma are Br(-) and, to a lesser extent, Cl(-), and their complexes with neutral halothane. APCI-TQ experiments indicated that Br(-) and Cl(-) are formed via reaction of halothane with O(2) (-.), O(2) (-.)(H(2)O) and O(3) (-.), possibly via dissociative electron transfer or nucleophilic substitution. Competing proton transfer was also observed in the reaction with O(2) (-.) and, at high halothane pressure, also with O(2) (-.)(H(2)O); at lower pressures the molecular anion M(-.) was observed instead. The other minor anions of the air plasma, NO(2) (-), N(2)O(2) (-.) and NO(3) (-), were found to be unreactive towards halothane.     

A fluorescent molecular imaging probe with selectivity for soluble tau aggregated protein

Soluble forms of aggregated tau misfolded protein, generally termed oligomers, are considered to be the most toxic species of the different assembly states that are the pathological components of neurodegenerative disorders. Therefore, a critical biomedical need exists for imaging probes that can identify and quantify them. We have designed and synthesized a novel fluorescent probe, pTP-TFE for which binding and selectivity profiles towards aggregated tau and Aβ proteins were assessed. Our results have shown pTP-TFE to be selective for early forms of soluble tau aggregates, with high affinity of dissociation constants (K_d) = 66 nM, and tenfold selectivity over mature tau fibrils. Furthermore, we found that pTP-TFE is selective for tau over Aβ aggregates and had good cell permeability. This selectivity of pTP-TFE towards early forms of aggregated tau protein ex vivo was also supported with studies on human brain tissue containing tau and Aβ pathology. To the best of our knowledge, this is the first fluorescent molecule to be reported to have this form of selectivity profile, which suggests that pTP-TFE is a unique probe candidate for imaging-based detection of early stages of Alzheimer''s disease and other tauopathies.

pTP-TFE imaging probe can distinguish soluble tau aggregated proteins from other aggregated proteins enabling earlier detection of neurodegenerative diseases.     

Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

Electrochemical Approach for the Production of Layered Double Hydroxides with a Well-Defined Co/MeIII Ratio

Layered double hydroxides (LDHs) have been widely studied for their plethora of fascinating features and applications. The potentiostatic electrodeposition of LDHs has been extensively applied in the literature as a fast and direct method to substitute classical chemical routes. However, the electrochemical approach does not usually allow for a fine control of the M^II/M^III ratio in the synthesized material. By employing a recently proposed potentiodynamic method, LDH films of controlled composition are herein prepared with good reproducibility, using different ratios of the trivalent (Fe or Al) to bivalent (Co) cations in the electrolytic solution. All the obtained materials are shown to be effective oxygen evolution reaction (OER) catalysts, and are thoroughly characterized by a multi-technique approach, including FE-SEM, XRD, Raman, AES and a wide range of electrochemical procedures.     

Monotonic bounds in multistage mixed-integer stochastic programming

Multistage stochastic programs bring computational complexity which may increase exponentially with the size of the scenario tree in real case problems. For this reason approximation techniques which replace the problem by a simpler one and provide lower and upper bounds to the optimal value are very useful. In this paper we provide monotonic lower and upper bounds for the optimal objective value of a multistage stochastic program. These results also apply to stochastic multistage mixed integer linear programs. Chains of inequalities among the new quantities are provided in relation to the optimal objective value, the wait-and-see solution and the expected result of using the expected value solution. The computational complexity of the proposed lower and upper bounds is discussed and an algorithmic procedure to use them is provided. Numerical results on a real case transportation problem are presented.