Exact Methods for Multistage Estimation of a Binomial Proportion

We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, we establish the uniform controllability of coverage probability and the asymptotic optimality for such a family of sampling schemes. Our theoretical results establish the possibility that the parameters of this family of sampling schemes can be determined so that the prescribed level of confidence is guaranteed with little waste of samples. Analytic bounds for the cumulative distribution functions and expectations of sample numbers are derived. Moreover, we discuss the inherent connection of various sampling schemes. Numerical issues are addressed for improving the accuracy and efficiency of computation. Computational experiments are conducted for comparing sampling schemes. Illustrative examples are given for applications in clinical trials.Comment: 38 pages, 9 figure

Methodology and Application of Adaptive and Sequential Approaches

The clinical trial, a prospective study to evaluate the effect of interventions in humans under prespecified conditions, is a standard and integral part of modern medicine. Many adaptive and sequential approaches have been proposed for use in clinical trials to allow adaptations or modifications to aspects of a trial after its initiation without undermining the validity and integrity of the trial. The application of adaptive and sequential methods in clinical trials has significantly improved the flexibility, efficiency, therapeutic effect, and validity of trials. To further advance the performance of clinical trials and convey the progress of research on adaptive and sequential methods in clinical trial design, we review significant research that has explored novel adaptive and sequential approaches and their applications in Phase I, II, and III clinical trials and discuss future directions in this field of research

Adaptive and Sequential Methods for Clinical Trials

This special issue describes state-of-the-art statistical research in adaptive and sequential methods and the application of such methods in clinical trials. It provides 1 review article and 5 research articles contributed by some of the leading experts in this field. The review article gives a comprehensive overview of the outstanding methodology in the current literature that is related to adaptive and sequential clinical trials, while each of the 5 research articles addresses specific critical issues in contemporary clinical trials, as summarized below

The multivariable finite elements based on B-spline wavelet on the interval for 1D structural mechanics

Wavelet finite elements with two kinds of variables for 1D structural mechanics are constructed based on B-spline wavelet on the interval (BSWI) and the generalized variational principle. In contrast to the traditional method, the BSWI element with two kinds of variables (TBSWI) can improve the solution accuracy of the generalized stress apparently, because generalized displacement and stress are interpolated separately. Another superiority of the elements constructed is the interpolating function BSWI, which has very good approximation property, further guarantees solution accuracy. Euler beam, Timoshenko beam and Elastic foundation beam are studied providing several numerical examples to verify the efficiency

Study of characteristic variations of high-speed spindles induced by centrifugal expansion deformations

High-speed machining has continuously pushed the demand of spindles with higher speed and higher reliability. In order to design, analyze, and test spindles in a virtual environment, accurate modeling of the spindle dynamics during the running state is essential. This paper investigates the variations of interference fit and bearing preload condition induced by centrifugal expansion deformations at high speed. Firstly, the elastic expansion deformations of the rotating parts due to centrifugal force are calculated based on mechanics of elasticity. It is found that the centrifugal expansion deformation of the bearing inner ring is much larger than the deformation of the shaft when the rotational speed increases, and therefore the amount of the interference between the shaft and the bearing decreases with the speed. Then, with consideration of the centrifugal expansion deformation, a dynamic model of high-speed rolling ball bearings is presented with experimental validation. With the proposed bearing model, centrifugal effects on the bearing preload condition are studied in detail. It is shown that the bearing contact angle decreases, while the contact load increases with the centrifugal expansion deformation of the bearing inner ring. The radial bearing stiffness increases, whereas the axial bearing stiffness decreases a little, due to the resultant effects of the decreased contact angle and the increased contact load. The preload condition of the spindle bearing is strengthened by the centrifugal expansion effect of the bearing inner ring

Simulation and Experimental Investigation of Structural Dynamic Frequency Characteristics Control

In general, mechanical equipment such as cars, airplanes, and machine tools all operate with constant frequency characteristics. These constant working characteristics should be controlled if the dynamic performance of the equipment demands improvement or the dynamic characteristics is intended to change with different working conditions. Active control is a stable and beneficial method for this, but current active control methods mainly focus on vibration control for reducing the vibration amplitudes in the time domain or frequency domain. In this paper, a new method of dynamic frequency characteristics active control (DFCAC) is presented for a flat plate, which can not only accomplish vibration control but also arbitrarily change the dynamic characteristics of the equipment. The proposed DFCAC algorithm is based on a neural network including two parts of the identification implement and the controller. The effectiveness of the DFCAC method is verified by several simulation and experiments, which provide desirable results

Quantifying Gauche Defects and Phase Evolution in Self-Assembled Monolayers through Sessile Drops

Self-assembled monolayers (SAMs) are widely used in surface modifications, specifically in tuning the surface chemistry of materials. The structure and properties of SAMs have been extensively studied often with sophisticated tools, even for the simplest n-alkanethiolate SAMs. In SAMs, especially in linear n-alkanethiolates, the properties are dependent on the chain length, which is best manifested in the so-called odd–even effect, a simple yet not fully understood phenomenon. One main challenge is fully delineating the origin of length-dependent properties, which can be due to the structure (ideal SAMs), defect evolution, or substrate-molecule effects. This study demonstrates that utilizing the wetting behavior of polar (water) and nonpolar (hexadecane (HD)) solvents on n-alkanethiolate SAMs formed on ultraflat gold and silver surfaces, the evolution of chain-length-dependent gauche defects can be revealed and parameterized through a newly defined dimensionless number (χ). The observation of the odd–even effect in hydrophobicity, however, depends on the thiol chain length, and it was only observed on longer-chain (\u3eC8) molecules. The trend in this odd–even effect demonstrates that there are three main transitions in the nature of wetting, hence structure, across n-alkanethiols. From wetting with HD, the role of dispersive components in wetting reveal that the SAMs are dynamic, which we attribute to rotations associated with previously reported evolution in gauche defects and changes in packing density. Therefore, from re-expression of the Young–Dupre equation, we define a new dimensionless number associated with molecular conformations, whose periodicity mirrors the energetics of Goodman’s conformations of n-alkanes in unbound states and associated four- or two-twist turns. Therefore, we infer that the evolution in surface energy is largely due to molecular conformations and associated relaxations of the bound thiolates

Effect of Substrate Morphology on the Odd–Even Effect in Hydrophobicity of Self-Assembled Monolayers

Surface roughness, often captured through root-mean-square roughness (Rrms), has been shown to impact the quality of self-assembled monolayers (SAMs) formed on coinage metals. Understanding the effect of roughness on hydrophobicity of SAMs, however, is complicated by the odd-even effect-a zigzag oscillation in contact angles with changes in molecular length. We recently showed that for surfaces with Rrms \u3e 1 nm, the odd-even effect in hydrophobicitycannot be empirically observed. In this report, we compare wetting properties of SAMs on Ag and Au surfaces of different morphologies across the Rrms similar to 1 nm limit. We prepared surfaces with comparable properties (grain sizes and Rrms) and assessed the wetting properties of resultant SAMs. Substrates with Rrms either below or above the odd-even limit were investigated. With smoother surfaces (lower Rrms), an inverted asymmetric odd-evenzigzag oscillation in static contact angles (?s) was observed with change from Au to Ag. Asymmetry in odd-even oscillation in Au was attributed to a larger change in ?s from odd to even number of carbons in the n-alkanethiol and vice versa for Ag. For rougher surfaces, no odd-even effect was observed; however, a gradual increase in the static contact angle was observed. Increase in the average grain sizes (\u3e3 times larger) on rough surfaces did not lead to significant difference in the wetting properties, suggesting that surface roughness significantly dominated the nature of the SAMs. We therefore infer that the predicted roughness-dependent limit to the observation of the odd-even effect in wetting properties of n-alkanethiols cannot be overcome by creating surfaces with large grain sizes for surfaces with Rrms \u3e 1 nm. We also observed that the differences between Au and Ag surfaces are dominated by differences in the even-numbered SAMs, but this difference vanishes with shorter molecular chain length (=C3)

Limits to the Effect of Substrate Roughness or Smoothness on the Odd–Even Effect in Wetting Properties of n-Alkanethiolate Monolayers

This study investigates the effect of roughness on interfacial properties of an n-alkanethiolate self-assembled monolayer (SAM) and uses hydrophobicity to demonstrate the existence of upper and lower limits. This article also sheds light on the origin of the previously unexplained gradual increase in contact angles with increases in the size of the molecule making the SAM. We prepared Au surfaces with a root-mean-square (RMS) roughness of ∼0.2–0.5 nm and compared the wetting properties of n-alkanethiolate (C10–C16) SAMs fabricated on these surfaces. Static contact angles, θs, formed between the SAM and water, diethylene glycol, and hexadecane showed an odd–even effect irrespective of the solvent properties. The average differences in subsequent SAME and SAMO are Δθs|n  – (n+1)| ≈ 1.7° (n = even) and Δθs|n – (n+1)| ≈ 3.1° (n = odd). A gradual increase in θs with increasing length of the molecule was observed, with values ranging from water 104.7–110.7° (overall Δθs = 6.0° while for the evens ΔθsE = 4.4° and odds ΔθsO = 3.5°) to diethylene glycol 72.9–80.4° (overall Δθs = 7.5° while for the evens ΔθsE = 2.9° and odds ΔθsO= 2.4°) and hexadecane 40.4–49.4° (overall Δθs = 9.0° while for the evens ΔθsE = 3.7° and odds ΔθsO = 2.1°). This article establishes that the gradual increase in θs with increasing molecular size in SAMs is due to asymmetry in the zigzag oscillation in the odd–even effect. Comparison of the magnitude and proportion differences in this asymmetry allows us to establish the reduction in interfacial dispersive forces, due to increasing SAM crystallinity with increasing molecular size, as the origin of this asymmetry. By comparing the dependence of θs on surface roughness we infer that (i) RMS roughness ≈ 1 nm is a theoretical limit beyond which the odd–even effect cannot be observed and (ii) on a hypothetically flat surface the maximum difference in hydrophobicity, as expressed in θs, is ∼3°

Early-season crop mapping using improved artificial immune network (IAIN) and Sentinel data

Substantial efforts have been made to identify crop types by region, but few studies have been able to classify crops in early season, particularly in regions with heterogeneous cropping patterns. This is because image time series with both high spatial and temporal resolution contain a number of irregular time series, which cannot be identified by most existing classifiers. In this study, we firstly proposed an improved artificial immune network (IAIN), and tried to identify major crops in Hengshui, China at early season using IAIN classifier and short image time series. A time series of 15-day composited images was generated from 10 m spatial resolution Sentinel-1 and Sentinel-2 data. Near-infrared (NIR) band and normalized difference vegetation index (NDVI) were selected as optimal bands by pair-wise Jeffries–Matusita distances and Gini importance scores calculated from the random forest algorithm. When using IAIN to identify irregular time series, overall accuracy of winter wheat and summer crops were 99% and 98.55%, respectively. We then used the IAIN classifier and NIR and NDVI time series to identify major crops in the study region. Results showed that winter wheat could be identified 20 days before harvest, as both the producer’s accuracy (PA) and user’s accuracy (UA) values were higher than 95% when an April 1–May 15 time series was used. The PA and UA of cotton and spring maize were higher than 95% with image time series longer than April 1–August 15. As spring maize and cotton mature in late August and September–October, respectively, these two crops can be accurately mapped 4–6 weeks before harvest. In addition, summer maize could be accurately identified after August 15, more than one month before harvest. This study shows the potential of IAIN classifier for dealing with irregular time series and Sentinel-1 and Sentinel-2 image time series at early-season crop type mapping, which is useful for crop management