Connections between Construction D and related constructions of lattices

Most practical constructions of lattice codes with high coding gains are multilevel constructions where each level corresponds to an underlying code component. Construction D, Construction \(\hbox {D}'\) , and Forney’s code formula are classical constructions that produce such lattices explicitly from a family of nested binary linear codes. In this paper, we investigate these three closely related constructions along with the recently developed Construction \(\hbox {A}'\) of lattices from codes over the polynomial ring \(\mathbb {F}_2[u]/u^a\) . We show that Construction by Code Formula produces a lattice packing if and only if the nested codes being used are closed under Schur product, thus proving the similarity of Construction D and Construction by Code Formula when applied to Reed–Muller codes. In addition, we relate Construction by Code Formula to Construction \(\hbox {A}'\) by finding a correspondence between nested binary codes and codes over \(\mathbb {F}_2[u]/u^a\) . This proves that any lattice constructible using Construction by Code Formula is also constructible using Construction \(\hbox {A}'\) . Finally, we show that Construction \(\hbox {A}'\) produces a lattice if and only if the corresponding code over \(\mathbb {F}_2[u]/u^a\) is closed under shifted Schur product.     

Silver Microelectrode Arrays for Direct Analysis of Hydrogen Peroxide in Low Ionic Strength Samples

Silver microelectrode arrays are fabricated by photolithography for a one-step analysis of H₂O₂ in low ionic strength samples. The effects of electrode length, width, band-to-band separation, connection height, and adhesion layer are evaluated. The developed sensor shows excellent repeatability (RSD=1.20 % (n=5)) and reproducibility (RSD=1.12 % (n=5)) with the linear range of 0.0–10.0 mM, the sensitivity of 9.84±0.34 μA mM⁻¹, and the detection limit of 22.69 μM. The sensor has been successfully applied to detect H₂O₂ directly without the addition of supporting electrolyte in synthetic urine, tap water, drinking water, and milk samples.     

Picolinic diamide pincers for transition metal complexation and their electrochemical properties

A series of novel molecular pincers was successfully synthesised by a copper-free Sonogashira coupling methodology. Complexation of the pincers with Cu(II), Ni(II) and Co(II) was performed in the presence of triethylamine. The formation of the desirable pincer ligands and complexes was confirmed by nuclear magnetic resonance spectroscopy, Fourier transform infrared spectroscopy and mass spectrometry. Electrochemical properties of the complexes of the target pincer dimers investigated by means of cyclic voltammetry suggested that the pincer dimers should be able to serve as an electron donor for phenyl-C61-butyric acid methyl ester and as an electron acceptor for poly(3-hexylthiophene) in bulk heterojunction solar cells.     

Particle size dependence of the electrochemical properties of SrMnO3 supercapacitor electrodes

Journal of Solid State Electrochemistry - In this letter, we report on the simple process of preparing perovskite oxide SrMnO3 and the studying of the size effect on electrochemical properties for...     

Pseudocodeword-free criterion for codes with cycle-free Tanner graph

Iterative decoding and linear programming decoding are guaranteed to converge to the maximum-likelihood codeword when the underlying Tanner graph is cycle-free. Therefore, cycles are usually seen as the culprit of low-density parity-check codes. In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant rows. Specifically, we characterize all parity-check matrices that are pseudocodeword-free for such class of codes.     

ABCDP: Approximate Bayesian Computation with Differential Privacy

We developed a novel approximate Bayesian computation (ABC) framework, ABCDP, which produces differentially private (DP) and approximate posterior samples. Our framework takes advantage of the sparse vector technique (SVT), widely studied in the differential privacy literature. SVT incurs the privacy cost only when a condition (whether a quantity of interest is above/below a threshold) is met. If the condition is sparsely met during the repeated queries, SVT can drastically reduce the cumulative privacy loss, unlike the usual case where every query incurs the privacy loss. In ABC, the quantity of interest is the distance between observed and simulated data, and only when the distance is below a threshold can we take the corresponding prior sample as a posterior sample. Hence, applying SVT to ABC is an organic way to transform an ABC algorithm to a privacy-preserving variant with minimal modification, but yields the posterior samples with a high privacy level. We theoretically analyzed the interplay between the noise added for privacy and the accuracy of the posterior samples. We apply ABCDP to several data simulators and show the efficacy of the proposed framework.     

Effect of fluoride and hydroxyl group on bioactivity of the anodized films prepared by two-step anodization at low current density

Titanium and its alloys are promising dental implant materials. In order to improve the bioactivity of the anodized films, the two-step anodization was performed to produce the films. The steps were performed at 0.2 mA/cm² for 30 min in electrolytes containing H₃PO₄/C₂H₅OH and H₃PO₄/C₂H₅OH/NH₄F, respectively. The anodized films were soaked in a simulated body fluid (SBF). The effects of surface roughness, hydroxyl groups, fluoride, and hydrophilicity groups on the bioactivity were investigated and were found on the anodized films formed under two-step anodization using 1 M H₃PO₄ + 80% V/V C₂H₅OH + 0.75 wt% NH₄F. The bioactivity evaluation showed that the combination of two-step anodization in NH₄F as an electrolyte induced a formation of apatite on the anodized films. The surface roughness, hydroxyl groups, and fluoride formed on the hydrophilic anodized films are found to be responsible for the rapid formation of hydroxyapatite during SBF soaking. This will be useful in various biomedical applications especially in dental implant procedures.