Gold,silver, and palladium nanoparticle/nano-agglomerate generation,collection, and characterization

Generation, collection, and characterization of gold, silver, and palladium nanoparticles and nano-agglomerates (collectively “nanoparticles”) have been explored. The nanoparticles were generated with a spark aerosol generator (Palas GFG-1000). They were collected using a deposition cell under diffusion and thermophoresis. The shapes and sizes of the deposited particles were measured using transmission electron microscopy (TEM). TEM images showed that the particles were in the range of 8–100 nm in diameter, and their shapes varied from nearly spherical to highly non-spherical. Thermophoresis enhanced the deposition of nanoparticles (over the diffusive or the isothermal deposition) in all cases. Further, the size distributions of the nanoparticles generated in the gas phase (aerosol) were measured using a scanning mobility particle sizer (SMPS 3080, TSI) spectrometer. The SMPS results show that an increase in the spark frequency of the generator shifted the size distributions of the nanoparticles to larger diameters, and the total particle mass production rate increased linearly with increase in the spark frequency. The computational fluid dynamics code Fluent (Ansys) was used to model the flow in the deposition cell, and the computed results conform to the observations.     

Almost sure convergence of sums of maxima and minima of positive random variables

For a sequence of independent and identically distributed positive random variables, the almost sure convergence of sums of maxima (when suitably normalized) to appropriate constants is proved for both bounded and unbounded random variables. A similar result is also proved for sums of minima of such variables.     

Asymptotics and bootstrap for inverse Gaussian regression

This paper studies regression, where the reciprocal of the mean of a dependent variable is considered to be a linear function of the regressor variables, and the observations on the dependent variable are assumed to have an inverse Gaussian distribution. The large sample theory for the pseudo maximum likelihood estimators is available in the literature, only when the number of replications increase at a fixed rate. This is inadequate for many practical applications. This paper establishes consistency and derives the asymptotic distribution for the pseudo maximum likelihood estimators under very general conditions on the design points. This includes the case where the number of replications do not grow large, as well as the one where there are no replications. The bootstrap procedure for inference on the regression parameters is also investigated.Research supported in part by NSF Grant DMS-9208066.Research supported in part by NSERC of Canada.     

Asymptotic theory for estimators under random censorship

Summary The product limit estimator of an unknown distributionF is represented as aU-statistic plus an error of the ordero(1/n). Using this, the maximum likelihood estimator of the specific risk rate in the time interval [0,M], is shown to admit a two term Edgeworth expansion. This risk rate for a specific cause of death is defined as the ratio of the probability of death, due to that particular cause, in the time interval [0,M], to the mean life time of an individual up to that time pointM. Similar expansions for the bootstrapped statistics are used to show that the bootstrap distribution, of the studentized estimator of the risk rate, approximates the sampling distribution better than the corresponding normal distribution.Research supported in part by NSA Grant MDA 904-90-H-1001 and by NSF Grant DMS-9007717     

Subsample and half-sample methods

Hartigan's subsample and half-sample methods are both shown to be inefficient methods of estimating the sampling distributions. In the sample mean case the bootstrap is known to correct for skewness. But irrespective of the population, the estimates based on the subsample method, have skewness factor zero. This problem persists even if we take only samples of size less than or equal to half of the original sample. For linear statistics it is possible to correct this by considering estimates based on subsamples of size n, when the sample size is n. In the sample mean case can be taken as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeimaiaab6% cacaqG1aGaaeikaiaabgdacaqGGaGaeyOeI0IaaeiiaiaabgdacaqG% VaWaaOaaaeaacaqG1aaaleqaaOGaaeykaaaa!3E8A!\[{\text{0}}{\text{.5(1 }} - {\text{ 1/}}\sqrt {\text{5}} {\text{)}}\]. In spite of these negative results, the half-sample method is useful in estimating the variance of sample quantiles. It is shown that this method gives as good an estimate as that given by the bootstrap method. A major advantage of the half-sample method is that it is shown to be robust in estimating the mean square error of estimators of parameters of a linear regression model when the errors are heterogeneous. Bootstrap is known to give inconsistent results in this case; although, it is more efficient in the case of homogeneous errors.Research supported in part by NSA Grant MDA904-90-H-1001 and by NASA Grant NAGW-1917.     

A note on bootstrapping the variance of sample quantile

Summary Letm _{n, p} denote thep-th quantile based onn observations and let λ _p denote the population quantile. In this paper consistency of the bootstrap estimate of variance of is established.     

Improved machine learning scoring functions for identification of Electrophorus electricus’s acetylcholinesterase inhibitors

Molecular Diversity - Structure-based drug design (SBDD) is an important in silico technique, used for the identification of enzyme inhibitors. Acetylcholinesterase (AChE), obtained from...     

Limit Processes with Independent Increments for the Ewens Sampling Formula

The Ewens sampling formula in population genetics can be viewed as a probability measure on the group of permutations of a finite set of integers. Functional limit theory for processes defined through partial sums of dependent variables with respect to the Ewens sampling formula is developed. Techniques from probabilistic number theory are used to establish necessary and sufficient conditions for weak convergence of the associated dependent process to a process with independent increments. Not many results on the necessity part are known in the literature.     

2D Monoelemental Germanene Quantum Dots: Synthesis as Robust Photothermal Agents for Photonic Cancer Nanomedicine

As a new family member of the emerging two‐dimensional (2D) monoelemental materials (Xenes), germanene has shown promising advantages over the prototypical 2D Xenes, such as black phosphorus (BP) and graphene. However, efficient manufacture of novel germanene nanostructures is still a challenge. Herein, a simple top‐down approach for the liquid‐exfoliation of ultra‐small germanene quantum dots (GeQDs) is presented. The prepared GeQDs possess an average lateral size of about 4.5 nm and thickness of about 2.2 nm. The functionalized GeQDs were demonstrated to be robust photothermal agents (PTAs) with outstanding photothermal conversion efficacy (higher than those of graphene and BPQDs), superior stability, and excellent biocompatibility. As a proof‐of‐principle, 2D GeQDs‐based PTAs were used in fluorescence/photoacoustic/photothermal‐imaging‐guided hyperpyrexia ablation of tumors. This work could expand the application of 2D germanene to the field of photonic cancer nanomedicine.