Abstract: A facility abnormality prediction model generation system includes: a data receiver receiving data of sensors of a facility previously obtained during an operation of the facility; an abnormality notification time predictor detecting a malfunction time of a malfunction of the facility based on the data of the sensors and determining an abnormality notification time for pre-notification of the malfunction of the facility based on the detected malfunction time; an optimal sensor combination calculator generating a chromosome based on the data of the sensors and performing a genetic algorithm using the generated chromosome to calculate an optimal sensor combination which is a combination of sensor data related to the determined abnormality notification time; and a facility abnormality prediction model generator generating a facility abnormality prediction model for the pre-notification of the malfunction of the facility, based on the optimal sensor combination.

Abstract: A facility abnormality prediction model generation system includes: a data receiver receiving data of sensors of a facility previously obtained during an operation of the facility; an abnormality notification time predictor detecting a malfunction time of a malfunction of the facility based on the data of the sensors and determining an abnormality notification time for pre-notification of the malfunction of the facility based on the detected malfunction time; an optimal sensor combination calculator generating a chromosome based on the data of the sensors and performing a genetic algorithm using the generated chromosome to calculate an optimal sensor combination which is a combination of sensor data related to the determined abnormality notification time; and a facility abnormality prediction model generator generating a facility abnormality prediction model for the pre-notification of the malfunction of the facility, based on the optimal sensor combination.

Abstract: There is provided a beta-shape, which is a compact structure for topology among spheres defining a blending surface of a sphere set. There is also provided a method of constructing the beta-shape, comprising: acquiring a Voronoi diagram of spheres; searching for partially accessible Voronoi edges; and obtaining faces of the beta-shape from the partially accessible Voronoi edges. Further, there is provided a method of utilizing the beta-shape to recognize pockets, which comprises the steps of acquiring the beta-shapes, and recognizing the pockets from the beta-shapes.

Abstract: Systems and methods for computing three-dimensional (3D) Euclidean Voronoi diagrams are disclosed. For some embodiments, a set of 3D objects is accessed, in which each 3D object is mathematically defined. Thereafter, a Voronoi region associated with each of the 3D objects is computed, thereby resulting in a complete Euclidean Voronoi diagram of the set of 3D objects. In some embodiments, the 3D objects are spheres, each of which is defined by a center and a radius. For other embodiments, the 3D objects are convex objects, each of which is mathematically-definable (e.g., cylinders, sphero-cylinders, etc.). Unlike prior approaches that suggested using a numerical approach to computing the Voronoi diagram, the present disclosure employs mathematical approaches for computing the Euclidean Voronoi diagram, thereby improving efficiency in the computation of the Euclidean Voronoi diagram.

Abstract: Systems and methods for computing three-dimensional (3D) Euclidean Voronoi diagrams are disclosed. For some embodiments, a set of 3D objects is accessed, in which each 3D object is mathematically defined. Thereafter, a Voronoi region associated with each of the 3D objects is computed, thereby resulting in a complete Euclidean Voronoi diagram of the set of 3D objects. In some embodiments, the 3D objects are spheres, each of which is defined by a center and a radius. For other embodiments, the 3D objects are convex objects, each of which is mathematically-definable (e.g., cylinders, sphero-cylinders, etc.). Unlike prior approaches that suggested using a numerical approach to computing the Voronoi diagram, the present disclosure employs mathematical approaches for computing the Euclidean Voronoi diagram, thereby improving efficiency in the computation of the Euclidean Voronoi diagram.

Abstract: In one embodiment, a system or method involves accessing a database having a macromolecular structure of a protein, the molecular structure being represented as a set of spheres, retrieving the molecular structure of the protein from the database, and mathematically computing a Euclidean Voronoi diagram representing atoms of the protein from the set of spheres.

Abstract: There is provided a beta-shape, which is a compact structure for topology among spheres defining a blending surface of a sphere set. There is also provided a method of constructing the beta-shape, comprising: acquiring a Voronoi diagram of spheres; searching for partially accessible Voronoi edges; and obtaining faces of the beta-shape from the partially accessible Voronoi edges. Further, there is provided a method of utilizing the beta-shape to recognize pockets, which comprises the steps of acquiring the beta-shapes, and recognizing the pockets from the beta-shapes.

Abstract: Systems and methods for computing three-dimensional (3D) Euclidean Voronoi diagrams are disclosed. For some embodiments, a set of 3D objects is accessed, in which each 3D object is mathematically defined. Thereafter, a Voronoi region associated with each of the 3D objects is computed, thereby resulting in a complete Euclidean Voronoi diagram of the set of 3D objects. In some embodiments, the 3D objects are spheres, each of which is defined by a center and a radius. For other embodiments, the 3D objects are convex objects, each of which is mathematically-definable (e.g., cylinders, sphero-cylinders, etc.). Unlike prior approaches that suggested using a numerical approach to computing the Voronoi diagram, the present disclosure employs mathematical approaches for computing the Euclidean Voronoi diagram, thereby improving efficiency in the computation of the Euclidean Voronoi diagram.