One-Step Generalized Estimating Equations With Large Cluster Sizes

Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.     

The Aqueous Ca2+ System,in Comparison with Zn2+, Fe3 +, and Al3 +: An Ab Initio Molecular Dynamics Study

Herein, we report on the structure and dynamics of the aqueous Ca²⁺ system studied by using ab initio molecular dynamics (AIMD) simulations. Our detailed study revealed the formation of well‐formed hydration shells with characteristics that were significantly different to those of bulk water. To facilitate a robust comparison with state‐of‐the‐art X‐ray absorption fine structure (XAFS) data, we employ a 1st principles MD‐XAFS procedure and directly compare simulated and experimental XAFS spectra. A comparison of the data for the aqueous Ca²⁺ system with those of the recently reported Zn²⁺, Fe³⁺, and Al³⁺ species showed that many of their structural characteristics correlated well with charge density on the cation. Some very important exceptions were found, which indicated a strong sensitivity of the solvent structure towards the cation′s valence electronic structure. Average dipole moments for the 2nd shell of all cations were suppressed relative to bulk water.     

Atomic Layer Deposition of Cobalt Phosphide for Efficient Water Splitting

Transition‐metal phosphides (TMP) prepared by atomic layer deposition (ALD) are reported for the first time. Ultrathin Co‐P films were deposited by using PH₃ plasma as the phosphorus source and an extra H₂ plasma step to remove excess P in the growing films. The optimized ALD process proceeded by self‐limited layer‐by‐layer growth, and the deposited Co‐P films were highly pure and smooth. The Co‐P films deposited via ALD exhibited better electrochemical and photoelectrochemical hydrogen evolution reaction (HER) activities than similar Co‐P films prepared by the traditional post‐phosphorization method. Moreover, the deposition of ultrathin Co‐P films on periodic trenches was demonstrated, which highlights the broad and promising potential application of this ALD process for a conformal coating of TMP films on complex three‐dimensional (3D) architectures.     

Developments in microscale and nanoscale sensors for biomedical sensing

The widespread use of point of care testing in biomedical and clinical applications is a major aim of the electrochemical field. A large number of groups are working on lab-on-a-chip systems or sensor arrays which are underpinned by electrochemical detection methodologies. Miniaturized transducers have the potential to be adopted in such systems for diagnosis of a range of diseases in both clinical and nonclinical settings. In this review, we will present the current trends and state of the art for a selection of miniaturized sensing elements (microelectrodes, nanoelectrodes, and field-effect transistors) and provide an impression of current technologies, their associated performance characteristics, and also considering the major barriers to adoption and how they might be surmounted in future so these technologies can fulfil their early promise.     

Computing Perelman?s ν-functional

This is a short note in which we show how to calculate the value of Perelman?s ν-functional for a variety of metrics. In particular we complete the calculation of values for the known 4-dimensional Einstein and shrinking Ricci soliton metrics.