Abstract: Performing sequencing of a polynucleotide. A first image of microparticles that are distributed in a random fashion on a substrate may be received. Each of the microparticles may include a plurality of similar oligonucleotides of the polynucleotide. A second image of the microparticles may be received. A plurality of first subportions of the first image may be determined. Each subportion may include a respective plurality of microparticles distributed in a random fashion. The second image may be analyzed to identify a plurality of second subportions in the second image. Each of the plurality of second subportions may correspond to a respective one of the plurality of first subportions. A plurality of the microparticles may be matched from the first and second images based on said analyzing. At least a portion of the sequence of nucleotides of the polynucleotide may be determined based on said matching.

Abstract: Performing sequencing of a polynucleotide. A first image of microparticles that are distributed in a random fashion on a substrate may be received. Each of the microparticles may include a plurality of similar oligonucleotides of the polynucleotide. A second image of the microparticles may be received. A plurality of first subportions of the first image may be determined. Each subportion may include a respective plurality of microparticles distributed in a random fashion. The second image may be analyzed to identify a plurality of second subportions in the second image. Each of the plurality of second subportions may correspond to a respective one of the plurality of first subportions. A plurality of the microparticles may be matched from the first and second images based on said analyzing. At least a portion of the sequence of nucleotides of the polynucleotide may be determined based on said matching.

Abstract: System and method for approximating a system. A multi-parameter representation of a family of systems is stored. An embedding of the family into an abstract geometrical continuous space with a metric and defined by the parameters is determined. Coordinates of the space specify values for the parameters of systems of the family. The space includes a grid of points representing respective discrete approximations of the systems. A first point corresponding to a desired instance of a system is determined. The first point's coordinates specify values for the parameters of the instance. The space is sampled using a mapping of a well-distributed point set from a Euclidean space of the parameters to the abstract space. A nearest discrete point to the first point is determined which specifies values for parameters for an optimal discrete approximation of the desired instance, which are useable to implement the discrete approximation of the desired instance.

Abstract: System and method for approximating a system. A multi-parameter representation of a family of systems is stored. An embedding of the family into an abstract geometrical continuous space with a metric and defined by the parameters is determined. Coordinates of the space specify values for the parameters of systems of the family. The space includes a grid of points representing respective discrete approximations of the systems. A first point corresponding to a desired instance of a system is determined. The first point's coordinates specify values for the parameters of the instance. The space is sampled using a mapping of a well-distributed point set from a Euclidean space of the parameters to the abstract space. A nearest discrete point to the first point is determined which specifies values for parameters for an optimal discrete approximation of the desired instance, which are useable to implement the discrete approximation of the desired instance.