Discrete Weierstrass-Type Representations

Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We show that the known discrete Weierstrass-type representations of certain surface classes can be viewed as applications of the Ω-dual transform to lightlike Gauss maps in Laguerre geometry. From this construction, further Weierstrass-type representations arise. As an application of the techniques we develop, we show that all discrete linear Weingarten surfaces of Bryant or Bianchi type locally arise via Weierstrass-type representations from discrete holomorphic maps.</p

SenStick: Comprehensive Sensing Platform with an Ultra Tiny All-In-One Sensor Board for IoT Research

We propose a comprehensive sensing platform called SenStick, which is composed of hardware (ultra tiny all-in-one sensor board), software (iOS, Android, and PC), and 3D case data. The platform aims to allow all the researchers to start IoT research, such as activity recognition and context estimation, easily and efficiently. The most important contribution is the hardware that we have designed. Various sensors often used for research are embedded in an ultra tiny board with the size of 50 mm (W) × 10 mm (H) × 5 mm (D) and weight around 3 g including a battery. Concretely, the following sensors are embedded on this board: acceleration, gyro, magnetic, light, UV, temperature, humidity, and pressure. In addition, this board has BLE (Bluetooth low energy) connectivity and capability of a rechargeable battery. By using 110 mAh battery, it can run more than 15 hours. The most different point from other similar boards is that our board has a large flash memory for logging all the data without a smartphone. By using SenStick, all the users can collect various data easily and focus on IoT data analytics. In this paper, we introduce SenStick platform and some case studies. Through the user study, we confirmed the usefulness of our proposed platform

Crystal structure of Grimontia hollisae collagenase provides insights into its novel substrate specificity toward collagen

Collagenase from the gram-negative bacterium Grimontia hollisae strain 1706B (Ghcol) degrades collagen more efficiently even than clostridial collagenase, the most widely used industrial collagenase. However, the structural determinants facilitating this efficiency are unclear. Here, we report the crystal structures of ligand-free and Gly-Pro-hydroxyproline (Hyp)-complexed Ghcol at 2.2 and 2.4 Å resolution, respectively. These structures revealed that the activator and peptidase domains in Ghcol form a saddle-shaped structure with one zinc ion and four calcium ions. In addition, the activator domain comprises two homologous subdomains, whereas zinc-bound water was observed in the ligand-free Ghcol. In the ligand-complexed Ghcol, we found two Gly-Pro-Hyp molecules, each bind at the active site and at two surfaces on the duplicate subdomains of the activator domain facing the active site, and the nucleophilic water is replaced by the carboxyl oxygen of Hyp at the P1 position. Furthermore, all Gly-Pro-Hyp molecules bound to Ghcol have almost the same conformation as Pro-Pro-Gly motif in model collagen (Pro-Pro-Gly)₁₀, suggesting these three sites contribute to the unwinding of the collagen triple helix. A comparison of activities revealed that Ghcol exhibits broader substrate specificity than clostridial collagenase at the P2 and P2′ positions, which may be attributed to the larger space available for substrate binding at the S2 and S2′ sites in Ghcol. Analysis of variants of three active-site Tyr residues revealed that mutation of Tyr564 affected catalysis, whereas mutation of Tyr476 or Tyr555 affected substrate recognition. These results provide insights into the substrate specificity and mechanism of G. hollisae collagenase