Abstract: Disclosed are embodiments for the generation of point clouds representing a region of space. The region may comprise a plurality of objects, which may comprise cubes, voxels, and/or the like. A plurality of points are calculated and distributed among the objects within the region. Generation of such point clouds may be useful in rendering representations of the region of space, and/or respective object(s) therein, on human-machine interface devices, such as computer displays and/or the like.

Abstract: Methods are provided for nucleic acid analysis. In an illustrative method, allele amplification bias is used to amplify preferentially a target nucleic acid that is present in a low allele fraction.

Abstract: Disclosed are embodiments for the generation of point clouds representing a region of space. The region may comprise a plurality of objects, which may comprise cubes, voxels, and/or the like. A plurality of points are calculated and distributed among the objects within the region. Generation of such point clouds may be useful in rendering representations of the region of space, and/or respective object(s) therein, on human-machine interface devices, such as computer displays and/or the like.

Abstract: Presented are embodiments for the generation of point clouds on a surface. A surface is described by a mathematical function. The surface may be subdivided into a plurality of patches, a plurality of triangles, or a plurality of rectangles, inter alia. A plurality of points are calculated and distributed among the patches, triangles, or rectangles comprising the surface. Generation of such point clouds may be useful in rendering N-dimensional surfaces for display or output on computer display or output devices.

Abstract: Presented are embodiments for the generation of point clouds on a surface. A surface is described by a mathematical function. The surface may be subdivided into a plurality of patches, a plurality of triangles, or a plurality of rectangles, inter alia. A plurality of points are calculated and distributed among the patches, triangles, or rectangles comprising the surface. Generation of such point clouds may be useful in rendering N-dimensional surfaces for display or output on computer display or output devices.

Abstract: Presented are embodiments for the generation of point clouds on a surface. A surface is described by a mathematical function. The surface may be subdivided into a plurality of patches, a plurality of triangles, or a plurality of rectangles, inter alia. A plurality of points are calculated and distributed among the patches, triangles, or rectangles comprising the surface. Generation of such point clouds may be useful in rendering N-dimensional surfaces for display or output on computer display or output devices.

Abstract: Novel and simple methods, systems, and computer program products for implementing a 3D rotation using input from a mouse, trackball, or other input device are described. Methods of implementing rotations are presented which lead to new realizations of the 3D rotation group and its double-cover, the unit quaternions. New methods, systems, and computer program products are also presented for interpolating rotations of a 3D scene that is more efficient than previously-known quaternion-based methods. The new methods are also used to derive the quaternion composition formula from the geometry of 3D rotations.

Abstract: Methods are provided for nucleic acid analysis. In an illustrative method, allele amplification bias is used to amplify preferentially a target nucleic acid that is present in a low allele fraction.

Abstract: Methods are provided for nucleic acid analysis. In an illustrative method, allele amplification bias is used to amplify preferentially a target nucleic acid that is present in a low allele fraction.

Abstract: An experimental melting curve is modeled as a sum of a true melting curve and background fluorescence. A deviation function may be generated based upon the experimental melting curve data and a model of a background signal. The deviation function may be generated by segmenting a range of the experimental curve into a plurality of windows. Within each window, a fit between the model of the background signal and the experimental melting curve data may be calculated. The deviation function may be formed from the resulting fit parameters. The deviation function may include background signal compensation and, as such, may be used in various melting curve analysis operations, such as data visualization, clustering, genotyping, scanning, negative sample removal, and the like. The deviation function may be used to seed an automated background correction process. A background-corrected melting curve may be further processed to remove an aggregation signal.

Abstract: An experimental melting curve is modeled as a sum of a true melting curve and background fluorescence. A deviation function may be generated based upon the experimental melting curve data and a model of a background signal. The deviation function may be generated by segmenting a range of the experimental curve into a plurality of windows. Within each window, a fit between the model of the background signal and the experimental melting curve data may be calculated. The deviation function may be formed from the resulting fit parameters. The deviation function may include background signal compensation and, as such, may be used in various melting curve analysis operations, such as data visualization, clustering, genotyping, scanning, negative sample removal, and the like. The deviation function may be used to seed an automated background correction process. A background-corrected melting curve may be further processed to remove an aggregation signal.

Abstract: Novel and simple methods, systems, and computer program products for implementing a 3D rotation using input from a mouse, trackball, or other input device are described. Methods of implementing rotations are presented which lead to new realizations of the 3D rotation group and its double-cover, the unit quaternions. New methods, systems, and computer program products are also presented for interpolating rotations of a 3D scene that is more efficient than previously-known quaternion-based methods. The new methods are also used to derive the quaternion composition formula from the geometry of 3D rotations.

Abstract: Novel and simple methods, systems, and computer program products for implementing a 3D rotation using input from a mouse, trackball, or other input device are described. Methods of implementing rotations are presented which lead to new realizations of the 3D rotation group and its double-cover, the unit quaternions. New methods, systems, and computer program products are also presented for interpolating rotations of a 3D scene that is more efficient than previously-known quaternion-based methods. The new methods are also used to derive the quaternion composition formula from the geometry of 3D rotations.

Abstract: A method for clustering melting profiles of a plurality of nucleic acid samples, comprising measuring the fluorescence of each nucleic acid sample as a function of temperature to produce a respective raw melting curve for each respective nucleic acid sample, and clustering genotypes of the plurality of nucleic acid samples to form a plurality of clusters of melting curves. A system for analyzing a plurality of nucleic acid samples comprising an instrument for sequentially heating fluorescently detectable complexes while monitoring their fluorescence, a central processing unit (CPU) for performing computer executable instructions, and a memory storage device for storing computer executable instructions that when executed by the CPU cause the CPU to cluster genotypes of a plurality of nucleic acid samples.

Abstract: A method for clustering melting profiles of a plurality of nucleic acid samples, comprising measuring the fluorescence of each nucleic acid sample as a function of temperature to produce a respective raw melting curve for each respective nucleic acid sample, and clustering genotypes of the plurality of nucleic acid samples to form a plurality of clusters of melting curves. A system for analyzing a plurality of nucleic acid samples comprising an instrument for sequentially heating fluorescently detectable complexes while monitoring their fluorescence, a central processing unit (CPU) for performing computer executable instructions, and a memory storage device for storing computer executable instructions that when executed by the CPU cause the CPU to cluster genotypes of a plurality of nucleic acid samples.

Abstract: Methods are provided for nucleic acid analysis. In an illustrative method, allele amplification bias is used to amplify preferentially a target nucleic acid that is present in a low allele fraction.

Abstract: A system and methods are provided for melting curve genotyping analysis of nucleic acids. Melting curves are generated by plotting fluorescence of a sample as a function of temperature. In one illustrative example, an exponential algorithm is employed to remove the background from generated melting curves and thereby perform comparative analysis to other melting curves. Additional illustrative examples provide for measuring the differences between two or more melting curves and clustering the genotypes of the provided sample nucleic acids.

Abstract: An experimental melting curve is modeled as a sum of a true melting curve and background fluorescence. A deviation function may be generated based upon the experimental melting curve data and a model of a background signal. The deviation function may be generated by segmenting a range of the experimental curve into a plurality of windows. Within each window, a fit between the model of the background signal and the experimental melting curve data may be calculated. The deviation function may be formed from the resulting fit parameters. The deviation function may include background signal compensation and, as such, may be used in various melting curve analysis operations, such as data visualization, clustering, genotyping, scanning, negative sample removal, and the like. The deviation function may be used to seed an automated background correction process. A background-corrected melting curve may be further processed to remove an aggregation signal.

Abstract: Presented are embodiments for the generation of point clouds on a surface. A surface is described by a mathematical function. The surface may be subdivided into a plurality of patches, a plurality of triangles, or a plurality of rectangles, inter alia. A plurality of points are calculated and distributed among the patches, triangles, or rectangles comprising the surface. Generation of such point clouds may be useful in rendering N-dimensional surfaces for display or output on computer display or output devices.

Abstract: Novel and simple methods, systems, and computer program products for implementing a 3D rotation using input from a mouse, trackball, or other input device are described. Methods of implementing rotations are presented which lead to new realizations of the 3D rotation group and its double-cover, the unit quaternions. New methods, systems, and computer program products are also presented for interpolating rotations of a 3D scene that is more efficient than previously-known quaternion-based methods. The new methods are also used to derive the quaternion composition formula from the geometry of 3D rotations.