Abstract: Method and system are provided for uncertainty quantification analysis with efficient two dimensional (2D) random fields. The method may be used in a modeling system. The method may include providing a covariance matrix of a set of parameters with a covariance function describing an occurring real world phenomenon; and generating a random field based on the covariance matrix including a controlled rank reduction to produce a reduced-rank random field dataset provided as a data structure with data compression. Generating the random field applies rank reduction of a block circulant with circulant blocks (BCCB) representation of a covariance matrix obtained from the covariance matrix using existing symmetry of eigenvalues to eliminate redundant computations. The method may include outputting a reduced-rank random field dataset for use in a user-provided model of the modeling system for uncertainty quantification analysis and simulation of the real world phenomenon.

Abstract: A navigation device including a housing including an opening, two or more drive wheels, and two or more rollers, a spherical member located within the opening of the housing in direct contact with the two or more drive wheels and the two or more rollers such that the drive wheels control rotation of the spherical member in response to guidance signals received from a processor, and an attachable member coupled directly to the housing for securing the navigation device to a body part of a user and maintaining contact between the user's skin and the spherical member.

Abstract: An apparatus, a method, and a computer program product for cleaning and collecting microplastics and modelling workflow for microplastic autonomous filtration. The apparatus may include a cleaning chamber through which water containing the microplastics flows. The apparatus may also include a transducer configured to generate microbubbles of a size that causes the microbubbles to clean microplastics flowing through the cleaning chamber. The apparatus may also include a filter chamber located above the cleaning chamber, where the filter chamber includes a microplastic collection device operable to collect the microplastics.

Abstract: An apparatus, a method, and a computer program product for cleaning and collecting microplastics and modelling workflow for microplastic autonomous filtration. The apparatus may include a cleaning chamber through which water containing the microplastics flows. The apparatus may also include a transducer configured to generate microbubbles of a size that causes the microbubbles to clean microplastics flowing through the cleaning chamber. The apparatus may also include a filter chamber located above the cleaning chamber, where the filter chamber includes a microplastic collection device operable to collect the microplastics.

Abstract: Method and system are provided for uncertainty quantification analysis with efficient two dimensional (2D) random fields. The method may be used in a modeling system. The method may include providing a covariance matrix of a set of parameters with a covariance function describing an occurring real world phenomenon; and generating a random field based on the covariance matrix including a controlled rank reduction to produce a reduced-rank random field dataset provided as a data structure with data compression. Generating the random field applies rank reduction of a block circulant with circulant blocks (BCCB) representation of a covariance matrix obtained from the covariance matrix using existing symmetry of eigenvalues to eliminate redundant computations. The method may include outputting a reduced-rank random field dataset for use in a user-provided model of the modeling system for uncertainty quantification analysis and simulation of the real world phenomenon.