Shot noise sets the limit of quantification in electrochemical measurements

Detection of single molecules, particles, and rapid redox events is a challenge of electrochemical investigations and requires either an amplification strategy or significant averaging for the electrochemical current to exceed the noise level. We consider the minimum number of electrons required to reach the limit of quantification in these electrochemical measurements. A survey of the literature indicates that the state-of-the-art limit in current detection for different types of measurements (e.g. voltammetry, single-molecule redox cycling, ion channel recordings of single molecules, metal nanoparticle collision, and phase nucleation) is independent of the nature of the measurement and increases linearly with reciprocal response time, Δt^?1, over ～5 orders of magnitude (from ～10 to ～10⁶ s^?1). We demonstrate that the practical limit of quantification requires cumulative measurement of ～2100 electrons during Δt and is determined by statistics of counting electrons, that is, the shot noise in the current.     

Development and application of a simple routine method for the determination of selenium in serum by octopole reaction system ICPMS

The aim of the study was to develop an inductively coupled plasma mass spectrometry (ICPMS) method for robust and simple routine determination of selenium in serum. Polyatomic interferences on ⁷⁶Se, ⁷⁷Se, and ⁷⁸Se were removed by applying an octopole reaction system ICPMS with the reaction cell pressurized with H₂ gas. We developed a novel simple optimization routine for the H₂ gas flow based on a signal-to-noise ratio (SNR) calculation of the selenium signal measured in a single selenium standard. The optimum H₂ flow was 2.9 mL min^–1. The selenium content in serum was determined after a 50-fold dilution with 0.16 M HNO₃ and quantified by using addition calibration and gallium as an internal standard. The method detection limit was 0.10 g L^–1 for ⁷⁶Se and ⁷⁸Se and 0.13 g L^–1 for ⁷⁷Se. Human serum samples from a case-control study investigating if selenium was associated with risk of colorectal adenoma were analyzed. The average selenium concentration for the control group (n=768) was 137.1 g L^–1 and the range was 73.4–305.5 g L^–1. The within-batch repeatability (a batch is ten samples) estimated from 182 replicate analyses was 6.3% coefficient of variation (CV), whereas the between-batch repeatability was 7.4% CV estimated from 361 replicates between batches. The method accuracy was evaluated by analysis of a human serum certified reference material (Seronorm Serum level II, Sero A/S, Norway). There was a fairly good agreement between the measured average of 145±3 g L^–1 (n=36) and the certified value of 136±9 g L^–1. In addition the method was successfully applied for analysis of zinc serum concentrations without further optimization. For the Seronorm certified reference material a value of 911±75 g L^–1 (n=31) for zinc was obtained, which corresponds well to the certified zinc value of 920±60 g L^–1.     

Optimal estimation of the diffusion coefficient from non-averaged and averaged noisy magnitude data

The magnitude operation changes the signal distribution in MRI images from Gaussian to Rician. This introduces a bias that must be taken into account when estimating the apparent diffusion coefficient. Several estimators are known in the literature. In the present paper, two novel schemes are proposed. Both are based on simple least squares fitting of the measured signal, either to the median (MD) or to the maximum probability (MP) value of the Probability Density Function (PDF). Fitting to the mean (MN) or a high signal-to-noise ratio approximation to the mean (HS) is also possible. Special attention is paid to the case of averaged magnitude images. The PDF, which cannot be expressed in closed form, is analyzed numerically. A scheme for performing maximum likelihood (ML) estimation from averaged magnitude images is proposed. The performance of several estimators is evaluated by Monte Carlo (MC) simulations. We focus on typical clinical situations, where the number of acquisitions is limited. For non-averaged data the optimal choice is found to be MP or HS, whereas uncorrected schemes and the power image (PI) method should be avoided. For averaged data MD and ML perform equally well, whereas uncorrected schemes and HS are inadequate. MD provides easier implementation and higher computational efficiency than ML. Unbiased estimation of the diffusion coefficient allows high resolution diffusion tensor imaging (DTI) and may therefore help solving the problem of crossing fibers encountered in white matter tractography.     

Interlaced Fourier transformation of ultrafast 2D NMR data

A new protocol for processing the data arising in ultrafast 2D NMR is discussed and exemplified, based on the interlaced Fourier transformation. This approach is capable of dealing in a single, combined fashion, with the two mirror-imaged interferograms arising in this kind of experiment as a result of the acquisition of a train of magnetic field gradient echoes. By combining all the acquired data points into a common Fourier processing procedure the spectral width along the direct-acquisition domain becomes effectively doubled, giving the opportunity of employing acquisition gradients that are approximately half as strong as hitherto required. This in turn should lead to an overall enhancement in the signal-to-noise ratio of the experiment of ca. 2, as well as to improvements in the achievable digital resolution. These expectations were tested by carrying out a series of homo- and heteronuclear ultrafast 2D NMR acquisitions, and found systematically fulfilled. The robustness and conditions that allow the interlaced numerical procedure to be implemented in routine analytical applications were explored and are briefly discussed.     

Planar microresonators for EPR experiments

EPR resonators on the basis of standing-wave cavities are optimised for large samples. For small samples it is possible to design different resonators that have much better power handling properties and higher sensitivity. Other parameters being equal, the sensitivity of the resonator can be increased by minimising its size and thus increasing the filling factor. Like in NMR, it is possible to use lumped elements; coils can confine the microwave field to volumes that are much smaller than the wavelength. We discuss the design and evaluation of EPR resonators on the basis of planar microcoils. Our test resonators, which operate at a frequency of 14 GHz, have excellent microwave efficiency factors, achieving 24 ns pi/2 EPR pulses with an input power of 17 mW. The sensitivity tests with DPPH samples resulted in the sensitivity value 2.3 x 10(9) spins.G(-1) Hz(-1/2) at 300 K.     

Optimal electric fields for different sample shapes in high resolution NMR spectroscopy

For many applications, reducing sample resistance, rather than increasing probe Q or filling factor, is the only way to further improve the signal-to-noise ratio of cryogenically cooled NMR probes. In this paper, bounds are calculated for the minimum sample resistance that can be achieved for various sample geometries. The sample resistance of 100 mM NaCl in H(2)O in 5 mm sample tubes was measured on a 600 MHz cold probe to be within 14% of the optimum value. The minimum sample resistance can however be lowered by altering the tube cross section. Rectangular tubes oriented with the long axis along the RF magnetic field are particularly favourable.     

Planar microcoil-based microfluidic NMR probes

Microfabricated small-volume NMR probes consisting of electroplated planar microcoils integrated on a glass substrate with etched microfluidic channels are fabricated and tested. 1H NMR spectra are acquired at 300 MHz with three different probes having observed sample volumes of respectively 30, 120, and 470 nL. The achieved sensitivity enables acquisition of an 1H spectrum of 160 microg sucrose in D2O, corresponding to a proof-of-concept for on-chip NMR spectroscopy. Increase of mass-sensitivity with coil diameter reduction is demonstrated experimentally for planar microcoils. Models that enable quantitative prediction of the signal-to-noise ratio and of the influence of microfluidic channel geometry on spectral resolution are presented and successfully compared to the experimental data. The main factor presently limiting sensitivity for high-resolution applications is identified as being probe-induced static magnetic field distortions. Finally, based on the presented model and measured data, future performance of planar microcoil-based microfluidic NMR probes is extrapolated and discussed.     

线型优化最大熵线性预测方法自回归模型三种求解方法的比较

采用三种方法：修正协方差法MCOV(Modified Covariance Method)、递推极大似然估计法RMLE(Recursive Maximum Likelihood Estimator)和伯格法(Burg Method)求解线型优化最大熵线性预测方法中的自回归模型系数,并且在不同求解方法情况下,将阶次、信噪比对光谱复原的影响作了详尽的比较.研究结果表明:在线型优化最大熵线性预测方法的自回归模型系数三种求解方法中,修正协方差法要优于递推极大似然估计法和伯格法.     

Parameter-induced stochastic resonance in an over-damped linear system

Stochastic resonance (SR) in an over-damped linear system subjected to an excitation of bias signal modulated noise with multiplicative and additive noises is investigated. We obtain the exact expressions of the first two moments and the signal-to-noise ratio (SNR) of the output by using linear-response theory. The SNR depends non-monotonically on the intensity and the correlation time of multiplicative noise, the correlation time of additive noise, the intensity of the cross noise between multiplicative and additive noise, as well as the external field frequency. The conventional SR, the SR in a broad sense and the bona fide SR are found in the system. The influences of the asymmetries of multiplicative and additive noise, the correlation rate of the cross noise, the intensity of additive noise, the amplitude of signal and the bias on the SNR are analyzed. Moreover, we pointed out that SR can be realized by tuning the system parameter with fixed noise, i.e., parameter-induced stochastic resonance (PSR) exists.     

大孔径静态干涉成像光谱仪的信噪比分析

根据大孔径静态干涉成像光谱仪的原理和特点，分析了光辐射能在光学系统内的传输情况，对探测器上接收到的光辐射能信号和噪音信号做了详细的推导，得到了仪器理论信噪比的表达式.在实验上以大口径积分球为辐射源，采集仪器输出的干涉图像，计算得到仪器的实际信噪比曲线，对大孔径静态干涉成像光谱仪的理论信噪比曲线与实际的信噪比曲线做分析比较，结果验证了用推导的论信噪比的表达式来预估仪器信噪比的可行性.