Fluorometric determination of paraoxon in human serum using a gold nanoparticle-immobilized organophosphorus hydrolase and coumarin 1 as a competitive inhibitor

A dimeric organophosphorus hydrolase (OPH; EC 3.1.8.1; 72 kDa) was isolated from wild-type bacteria, analyzed for its 16s rRNA sequence, purified, and immobilized on gold nanoparticles (AuNPs) to form the transducer part of a biosensor. The isolated strain was identified as Pseudomonas aeruginosa. The AuNPs were characterized by transmission electron microscopy and localized surface plasmon resonance. Covalent binding of OPH to the AuNPs was confirmed by spectrophotometry, enzymatic activity assays, and FTIR spectroscopy. Coumarin 1, a competitive inhibitor of OPH, was used as a fluorogenic probe. The bioconjugates quench the emission of coumarin 1 upon binding, but the addition of paraoxon results in an enhancement of fluorescence that is directly proportional to the concentration of paraoxon. The gold-OPH conjugates were then used to determine paraoxon in serum samples spiked with varying levels of paraoxon. The method works in the 50 to 1,050 nM concentration range, has a low standard deviation (with a CV of 5.7–11 %), and a detection limit as low as 5?×?10^?11 M.

Evidence for specular reflection in thin tungsten wires

A generalized version of the Nordheim model, appropriate to a metal with an anisotropic electron mean-free-path, is used to derive a lower bound upon the resistivity of a wire of diameterd when scattering from the wire surface is completely diffuse. Measurements of the electrical resistivities of thin tungsten wires are presented and shown to fall below this lower bound. These measurements are therefore inconsistent with the existence of completely diffuse surface scattering. Within the framework of the model, the data determine an amount of specular scattering specified by a specularity parameter of magnitudep≧0.2.     

Harmonic analysis of additive Lévy processes

Let X ₁, . . . ,X _N denote N independent d-dimensional Lévy processes, and consider the N-parameter random field $$\mathfrak{X}(t) := X_1(t_1)+\cdots+ X_N(t_N).$$ First we demonstrate that for all nonrandom Borel sets ${F\subseteq{{\bf R}^d}}$ , the Minkowski sum ${\mathfrak{X}({{\bf R}^{N}_{+}})\oplus F}$ , of the range ${\mathfrak{X}({{\bf R}^{N}_{+}})}$ of ${\mathfrak{X}}$ with F, can have positive d-dimensional Lebesgue measure if and only if a certain capacity of F is positive. This improves our earlier joint effort with Yuquan Zhong by removing a certain condition of symmetry in Khoshnevisan et al. (Ann Probab 31(2):1097–1141, 2003). Moreover, we show that under mild regularity conditions, our necessary and sufficient condition can be recast in terms of one-potential densities. This rests on developing results in classical (non-probabilistic) harmonic analysis that might be of independent interest. As was shown in Khoshnevisan et al. (Ann Probab 31(2):1097–1141, 2003), the potential theory of the type studied here has a large number of consequences in the theory of Lévy processes. Presently, we highlight a few new consequences.     

Bounds on Gambler's Ruin Probabilities in Terms of Moments

Consider a wager that is more complicated than simply winning or losing the amount of the bet. For example, a pass line bet with double odds is such a wager, as is a bet on video poker using a specified drawing strategy. We are concerned with the probability that, in an independent sequence of identical wagers of this type, the gambler loses L or more betting units (i.e., the gambler is ruined) before he wins W or more betting units. Using an idea of Markov, Feller established upper and lower bounds on the probability of ruin, bounds that are often very close to each other. However, his formulation depends on finding a positive nontrivial root of the equation ( )=1, where is the probability generating function for the wager in question. Here we give simpler bounds, which rely on the first few moments of the specified wager, thereby making such gambler's ruin probabilities more easily computable.     

Fe~(3+)-Doped Anatase TiO_2 Study Prepared by New Sol-Gel Precursors

FeTi_1-O_2(= 0.00,0.05,0.10) nanocomposites are synthesized using a sol-gel method involving an ethanol solvent in the presence of ethylene glycol as the stabilizer,and acetic acid as the chemical reagent.Their structural and optical analyses are studied to reveal their physicochemical properties.Using the x-ray diffractometer(XRD)analysis,the size of the nanoparticles(NPs) is found to be 18–32 nm,where the size of the NPs decreases down to 18 nm when Fe impurity of up to 10% is added,whereas their structure remains unchanged.The results also indicate that the structure of the NPs is tetragonal in the anatase phase.The Fourier transform infrared spectroscopy analysis suggests the presence of a vibration bond(Ti–O) in the sample.The photoluminescence analysis indicates that the diffusion of Fe~(3+) ions into the TiO_2 matrix results in a decreasing electron–hole recombination,and increases the photocatalytic properties,where the best efficiency appears at an impurity of10%.The UV-diffuse reflection spectroscopy analysis indicates that with the elevation of iron impurity,the band gap value decreases from 3.47 eV for the pure sample to 2.95 eV for the 10 mol% Fe-doped TiO_2 NPs.     

Dynamical percolation on general trees

Häggström et al. (Ann Inst H Poincaré Probab Stat 33(4):497–528, 1997) have introduced a dynamical version of percolation on a graph G. When G is a tree they derived a necessary and sufficient condition for percolation to exist at some time t. In the case that G is a spherically symmetric tree (Peres and Steif in Probab Theory Relat Fields 111(1):141–165, 1998), derived a necessary and sufficient condition for percolation to exist at some time t in a given target set D. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time ${t\in D}H?ggstr?m et al. (Ann Inst H Poincaré Probab Stat 33(4):497–528, 1997) have introduced a dynamical version of percolation on a graph G. When G is a tree they derived a necessary and sufficient condition for percolation to exist at some time t. In the case that G is a spherically symmetric tree (Peres and Steif in Probab Theory Relat Fields 111(1):141–165, 1998), derived a necessary and sufficient condition for percolation to exist at some time t in a given target set D. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time , in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation. Research supported in part by a grant from the National Science Foundation.     

Intersections of Brownian motions

This article presents a survey of the theory of the intersections of Brownian motion paths. Among other things, we present a truly elementary proof of a classical theorem of A. Dvoretzky, P. Erdős and S. Kakutani. This proof is motivated by old ideas of P. Lévy that were originally used to investigate the curve of planar Brownian motion.     

On the chaotic character of the stochastic heat equation, II

Consider the stochastic heat equation ${\partial_t u = (\varkappa/2)\Delta u+\sigma(u)\dot{F}}$ , where the solution u := u _t (x) is indexed by ${(t, x) \in (0, \infty) \times {\bf R}^d}$ , and ${\dot{F}}$ is a centered Gaussian noise that is white in time and has spatially-correlated coordinates. We analyze the large- ${\|x\|}$ fixed-t behavior of the solution u in different regimes, thereby study the effect of noise on the solution in various cases. Among other things, we show that if the spatial correlation function f of the noise is of Riesz type, that is ${f(x)\propto \|x\|^{-\alpha}}$ , then the “fluctuation exponents” of the solution are ${\psi}$ for the spatial variable and ${2\psi-1}$ for the time variable, where ${\psi:=2/(4-\alpha)}$ . Moreover, these exponent relations hold as long as ${\alpha \in (0, d \wedge 2)}$ ; that is precisely when Dalang’s theory [Dalang, Electron J Probab 4:(Paper no. 6):29, 1999] implies the existence of a solution to our stochastic PDE. These findings bolster earlier physical predictions [Kardar et al., Phys Rev Lett 58(20):889–892, 1985; Kardar and Zhang, Phys Rev Lett 58(20):2087–2090, 1987].     

Exceptional times and invariance for dynamical random walks

Consider a sequence of i.i.d. random variables. Associate to each X _i (0) an independent mean-one Poisson clock. Every time a clock rings replace that X-variable by an independent copy and restart the clock. In this way, we obtain i.i.d. stationary processes {X _i (t)} _{t ≥0} (i=1,2,···) whose invariant distribution is the law ν of X ₁(0). Benjamini et al. (2003) introduced the dynamical walk S _n (t)=X ₁(t)+···+X _n (t), and proved among other things that the LIL holds for n↦S _n (t) for all t. In other words, the LIL is dynamically stable. Subsequently (2004b), we showed that in the case that the X _i (0)'s are standard normal, the classical integral test is not dynamically stable. Presently, we study the set of times t when n↦S _n (t) exceeds a given envelope infinitely often. Our analysis is made possible thanks to a connection to the Kolmogorov ɛ-entropy. When used in conjunction with the invariance principle of this paper, this connection has other interesting by-products some of which we relate. We prove also that the infinite-dimensional process converges weakly in to the Ornstein–Uhlenbeck process in For this we assume only that the increments have mean zero and variance one. In addition, we extend a result of Benjamini et al. (2003) by proving that if the X _i (0)'s are lattice, mean-zero variance-one, and possess (2+ɛ) finite absolute moments for some ɛ>0, then the recurrence of the origin is dynamically stable. To prove this we derive a gambler's ruin estimate that is valid for all lattice random walks that have mean zero and finite variance. We believe the latter may be of independent interest. The research of D. Kh. is partially supported by a grant from the NSF.