Signature functions of knots

The signature function of a knot is an integer-valued step function on the unit circle in the complex plane. Necessary and sufficient conditions for a function to be the signature function of a knot are presented.Comment: 4 page

Deep-Learning-Enabled Fast Optical Identification and Characterization of Two-Dimensional Materials

Advanced microscopy and/or spectroscopy tools play indispensable role in nanoscience and nanotechnology research, as it provides rich information about the growth mechanism, chemical compositions, crystallography, and other important physical and chemical properties. However, the interpretation of imaging data heavily relies on the "intuition" of experienced researchers. As a result, many of the deep graphical features obtained through these tools are often unused because of difficulties in processing the data and finding the correlations. Such challenges can be well addressed by deep learning. In this work, we use the optical characterization of two-dimensional (2D) materials as a case study, and demonstrate a neural-network-based algorithm for the material and thickness identification of exfoliated 2D materials with high prediction accuracy and real-time processing capability. Further analysis shows that the trained network can extract deep graphical features such as contrast, color, edges, shapes, segment sizes and their distributions, based on which we develop an ensemble approach topredict the most relevant physical properties of 2D materials. Finally, a transfer learning technique is applied to adapt the pretrained network to other applications such as identifying layer numbers of a new 2D material, or materials produced by a different synthetic approach. Our artificial-intelligence-based material characterization approach is a powerful tool that would speed up the preparation, initial characterization of 2D materials and other nanomaterials and potentially accelerate new material discoveries

Sequencing of Culex quinquefasciatus establishes a platform for mosquito comparative genomics

Culex quinquefasciatus (the southern house mosquito) is an important mosquito vector of viruses such as West Nile virus and St. Louis encephalitis virus, as well as of nematodes that cause lymphatic filariasis. C. quinquefasciatus is one species within the Culex pipiens species complex and can be found throughout tropical and temperate climates of the world. The ability of C. quinquefasciatus to take blood meals from birds, livestock, and humans contributes to its ability to vector pathogens between species. Here, we describe the genomic sequence of C. quinquefasciatus: Its repertoire of 18,883 protein-coding genes is 22% larger than that of Aedes aegypti and 52% larger than that of Anopheles gambiae with multiple gene-family expansions, including olfactory and gustatory receptors, salivary gland genes, and genes associated with xenobiotic detoxification

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Effects of Injection Molding Parameters on Properties of Insert-Injection Molded Polypropylene Single-Polymer Composites

The reinforcement and matrix of a polymer material can be composited into a single polymer composite (SPC), which is light weight, high strength, and has easy recyclability. The insert injection molding process can be used to realize the multiple production of SPC products with a short cycle time and wide processing temperature window. However, injection molding is a very complicated process; the influence of several important parameters should be determined to help in the future tailoring of SPCs to specific applications. The effects of varying barrel temperature, injection pressure, injection speed, and holding time on the properties of the insert-injection molded polypropylene (PP) SPC parts were investigated. It was found that the sample weight and tensile properties of the PP SPCs varied in different rules with the variations of these four parameters. The barrel temperature has a significant effect, followed by the holding time and injection pressure. Suitable parameter values should be determined for enhanced mechanical properties. Based on the tensile strength, a barrel temperature of 260 °C, an injection pressure of 127.6 MPa, an injection speed of 0.18 m/s, and a holding time of 60 s were determined as the optimum processing conditions. The best tensile strength and peel strength were up to 120 MPa and 19.44 N/cm, respectively

A Proposed Bearing Load Identification Method to Uncertain Rotor Systems

Bearings are considered as important mechanical components in rotating machines. Bearing load is used as an indication of monitoring rotor system health, but there are interval and probability uncertain parameters in the process of obtaining bearing load from the rotor system. A bearing load strip enclosed by two bounding distributions is then formed, rather than a single distribution that we usually obtain through the load identification method for a deterministic rotor system. In this paper, a computational inverse approach that combines the interval and perturbation analysis method with regularization is presented to stably identify bearing load strip. Using an interval analysis method, a calculated transient response of the rotor structure only subjecting to the bearing load can be approximated as a linear function of the interval parameters in the rotor system. The perturbation analysis method based on Taylor expansion is used to transform the problem of the bearing load identification involving in probability parameters into two kinds of certain inverse problem, namely, the bearing load identification combining the mean value of uncertain parameters with calculated transient response function and the sensitivity identification of bearing load to each probability parameter. Regularization is used to overcome ill-posedness of bearing load identification arising from the noise-contaminated observed response. A rotor system with two bearings is investigated to demonstrate the effectiveness and accuracy of the presented method

Synthetic Variation and Structural Trends in Layered Two-Dimensional Alkylammonium Lead Halide Perovskites

We report the cooling-induced crystallization of layered two-dimensional lead halide perovskites with controllable inorganic quantum-well thickness (n = 1, 2, 3, 4), organic spacer chain length (butyl-, pentyl-, hexylammonium), A-site cation (methylammonium, formamidinium), and halide anion (iodide, bromide). We report crystal structures for the iodide family as a function of these compositional parameters, and across their temperature dependent phase transitions. In general, lower symmetry crystal structures, increasing extents of organic-spacer interdigitation, and increasing organic-spacer corrugation tilts are observed at low temperature. In addition, greater structural distortions are seen in lead halide octahedra closest to the organic spacer layer, and larger-n­ structures exhibit periodic variation in Pb-I bond lengths. We also provide detailed guidance regarding the combination of synthetic parameters needed to achieve phase-pure crystals of each composition, and discuss difficulties encountered when trying to synthesize particular members of the 2D perovskite family containing formamidinium or cesium as the A-site cation. These results provide a foundation for understanding structural trends in 2D lead halide perovskites and the effect these trends have on their thermal, electrical, and optical properties