The satisfiability threshold for random linear equations

Let $A$ be a random $m\times n$ matrix over the finite field $F_q$ with precisely $k$ non-zero entries per row and let $y\in F_q^m$ be a random vector chosen independently of $A$. We identify the threshold $m/n$ up to which the linear system $A x=y$ has a solution with high probability and analyse the geometry of the set of solutions. In the special case $q=2$, known as the random $k$-XORSAT problem, the threshold was determined by [Dubois and Mandler 2002, Dietzfelbinger et al. 2010, Pittel and Sorkin 2016], and the proof technique was subsequently extended to the cases $q=3,4$ [Falke and Goerdt 2012]. But the argument depends on technically demanding second moment calculations that do not generalise to $q>3$. Here we approach the problem from the viewpoint of a decoding task, which leads to a transparent combinatorial proof

Metal-catalyst-free growth of silica nanowires and carbon nanotubes using Ge nanostructures

The use of Ge nanostructures is investigated for the metal-catalyst-free growth of silica nanowires and carbon nanotubes (CNTs). Silica nanowires with diameters of 10-50 nm and lengths of ? 1 ?m were grown from SiGe islands, Ge dots, and Ge nanoparticles. High-resolution transmission electron microscopy (HRTEM) and energy dispersive X-ray spectroscopy (EDS) reveal that the nanowires grow from oxide nanoparticles on the sample surface. We propose that the growth mechanism is thermal diffusion of oxide through the GeO2 nanostructures. CNTs with diameters 0.6-2.5 nm and lengths of less than a few ?m were similarly grown by chemical vapor deposition from different types of Ge nanostructures. Raman measurements show the presence of radial breathing mode peaks and the absence of the disorder induced D-band, indicating single walled CNTs with a low defect density. HRTEM images reveal that the CNTs also grow from oxide nanoparticles, comprising a mixture of GeO2 and SiO2

Growth of Carbon Nanotubes on HfO2 towards Highly Sensitive Nano-Sensors

Carbon nanotube (CNT) growth on HfO2 is reported for the first time. The process uses a combination of Ge and Fe nanoparticles and achieves an increase in CNT density from 0.15 to 6.2 mm length/mm2 compared with Fe nanoparticles alone. The synthesized CNTs are assessed by the fabrication of back-gate CNT field-effect transistors with Al source/drain contacts for nano-sensor applications. The devices exhibit excellent p-type behavior with an Ion=Ioff ratio of 105 and a steep sub-threshold slope of 130 mV/dec

Parameters controlling octadecyl phosphonic acid self-assembled monolayers on titanium dioxide for anti-fouling biomedical applications

Octadecylphosphonic acid (ODPA) self-assembled monolayers (SAMs) have demonstrated potential for deterring bacterial attachment to titanium, however the coating process is time consuming and uses toxic solvents. In this study, ODPA SAM quantity, quality, and structure were evaluated on titanium quartz crystal microbalance (QCM) sensors by varying solvent type (anisole or cyclopentyl methyl ether (CPME), environmentally friendly non-polar solvents); ODPA concentration (0.5 mM or 1 mM); and temperature (21 °C or 60 °C). Surfaces were characterised using QCM frequency and dissipation measurements and Sauerbrey mass calculations; X-ray photoelectron spectroscopy; water contact angle measurements; and temperature-programmed desorption mass spectrometry (TPD-MS). Anti-fouling ability was established against Staphylococcus aureus. Incubation in 0.5 mM ODPA in CPME at 21 °C rapidly formed uniform rigid ODPA SAMs as demonstrated by high Sauerbrey mass (≈285-290 ng/cm2), viscoelastic modelling, high atomic percentage surface phosphorus (1.1 %) and high water contact angles (117.6 ± 2.5°), consistent across the entire sample surface. High temperatures or the use of anisole resulted in suspected multilayer formation, which reduced bacterial attachment. TPD-MS confirmed covalent bonding of ODPA SAMs on TiO2 at ≈ 110–120 °C and thermal stability below 300 °C. This study demonstrates the key parameters that control ODPA SAM formation on titanium and their future potential for biomedical applications

Criteria for effective zero-deforestation commitments

Zero-deforestation commitments are a type of voluntary sustainability initiative that companies adopt to signal their intention to reduce or eliminate deforestation associated with commodities that they produce, trade, and/or sell. Because each company defines its own zero-deforestation commitment goals and implementation mechanisms, commitment content varies widely. This creates challenges for the assessment of commitment implementation or effectiveness. Here, we develop criteria to assess the potential effectiveness of zero-deforestation commitments at reducing deforestation within a company supply chain, regionally, and globally. We apply these criteria to evaluate 52 zero-deforestation commitments made by companies identified by Forest 500 as having high deforestation risk. While our assessment indicates that existing commitments converge with several criteria for effectiveness, they fall short in a few key ways. First, they cover just a small share of the global market for deforestation-risk commodities, which means that their global impact is likely to be small. Second, biome-wide implementation is only achieved in the Brazilian Amazon. Outside this region, implementation occurs mainly through certification programs, which are not adopted by all producers and lack third-party near-real time deforestation monitoring. Additionally, around half of all commitments include zero-net deforestation targets and future implementation deadlines, both of which are design elements that may reduce effectiveness. Zero-net targets allow promises of future reforestation to compensate for current forest loss, while future implementation deadlines allow for preemptive clearing. To increase the likelihood that commitments will lead to reduced deforestation across all scales, more companies should adopt zero-gross deforestation targets with immediate implementation deadlines and clear sanction-based implementation mechanisms in biomes with high risk of forest to commodity conversion.ISSN:0959-3780ISSN:1872-949