Abstract: A method includes identifying multiple apportionments, where each apportionment identifies numbers of bit copies to be stored in at least one memory for at least some bits of a data value. The method also includes, for each apportionment, estimating a numerical error associated with use of the apportionment with a specified function, where the numerical error is estimated by creating errors in bit copies of multiple data values processed using the specified function. The method further includes combining portions of different ones of the apportionments having lower estimated numerical errors to create multiple derived apportionments. The method also includes, for each derived apportionment, estimating a numerical error associated with use of the derived apportionment with the specified function. In addition, the method includes selecting a final apportionment for use with the specified function, where the final apportionment includes or is based on at least one of the derived apportionments.

Abstract: A method includes identifying multiple apportionments, where each apportionment identifies numbers of bit copies to be stored in at least one memory for at least some bits of a data value. The method also includes, for each apportionment, estimating a numerical error associated with use of the apportionment with a specified function, where the numerical error is estimated by creating errors in bit copies of multiple data values processed using the specified function. The method further includes combining portions of different ones of the apportionments having lower estimated numerical errors to create multiple derived apportionments. The method also includes, for each derived apportionment, estimating a numerical error associated with use of the derived apportionment with the specified function. In addition, the method includes selecting a final apportionment for use with the specified function, where the final apportionment includes or is based on at least one of the derived apportionments.

Abstract: A method includes storing one or more bit copies of each of at least some bits of a data value in at least one memory. A number of bit copies of each bit of the data value is based on a specified apportionment, and different bits have different numbers of bit copies. The method also includes retrieving the bit copies of the at least some of the bits of the data value from the at least one memory. The method further includes, in response to determining that a specified bit of the data value has multiple retrieved bit copies that differ from one another, estimating a bit value for the specified bit using the multiple retrieved bit copies of the specified bit. In addition, the method includes outputting or using the data value having the estimated bit value for the specified bit.

Abstract: A method includes storing one or more bit copies of each of at least some bits of a data value in at least one memory. A number of bit copies of each bit of the data value is based on a specified apportionment, and different bits have different numbers of bit copies. The method also includes retrieving the bit copies of the at least some of the bits of the data value from the at least one memory. The method further includes, in response to determining that a specified bit of the data value has multiple retrieved bit copies that differ from one another, estimating a bit value for the specified bit using the multiple retrieved bit copies of the specified bit. In addition, the method includes outputting or using the data value having the estimated bit value for the specified bit.

Abstract: A facial recognition system and a method for performing facial recognition are provided. The facial recognition system includes a memory configured to store a target data set identifying a plurality of predefined points on a face of a target and a processor. The processor may be configured to receive an arbitrary number of photographs including a face of a subject, each of the photographs being at an arbitrary angle and at an arbitrary distance from the subject, create a subject data set identifying the plurality of predefined points on the subject's face based upon the received photographs, and perform facial recognition on the subject data set by comparing the subject data set to the target data set.

Abstract: In order to target and intercept a desired object within a number of objects detected in an environment, detection data is received from two different sensors, where the detection data includes spatial coordinates. A set of four-point subsets (tetrahedra) are selected from each set of spatial coordinates. A number of correlation maps are determined between the first set of spatial coordinates and the second set of spatial coordinates based on the plurality of four-point subsets. The mean sphericity for each corresponding plurality of four-point subsets in the plurality of correlation maps is determined, and a threat object map based on the correlation map having the greatest mean sphericity is created. The desired object is targeted based on the correlation map.

Abstract: A facial recognition system and a method for performing facial recognition are provided. The facial recognition system includes a memory configured to store a target data set identifying a plurality of predefined points on a face of a target and a processor. The processor may be configured to receive an arbitrary number of photographs including a face of a subject, each of the photographs being at an arbitrary angle and at an arbitrary distance from the subject, create a subject data set identifying the plurality of predefined points on the subject's face based upon the received photographs, and perform facial recognition on the subject data set by comparing the subject data set to the target data set.

Abstract: In order to target and intercept a desired object within a number of objects detected in an environment, detection data is received from two different sensors, where the detection data includes spatial coordinates. A set of four-point subsets (tetrahedra) are selected from each set of spatial coordinates. A number of correlation maps are determined between the first set of spatial coordinates and the second set of spatial coordinates based on the plurality of four-point subsets. The mean sphericity for each corresponding plurality of four-point subsets in the plurality of correlation maps is determined, and a threat object map based on the correlation map having the greatest mean sphericity is created. The desired object is targeted based on the correlation map.

Abstract: A slicing tool works with a solid modeling system to partition the geometric representation of a three-dimensional part into a series of simpler sub-parts the union of which replicates the original part in a manner that introduces a minimal number of new surfaces in each sub-part and in total. This approach uses the existing analytic surfaces that define the part geometry to partition the part and selects a partition from a quality metric based on the number of trimmed surfaces of the part being partitioned and the candidate sub-parts. This approach greatly reduces the complexity of any downstream solid modeling applications that perform combinatorial surface operations on the geometric representation of the series of sub-parts to analyze physical characteristics such as radiation, mechanical, optical, thermal, structural or biological of the original part.

Abstract: A slicing tool works with a solid modeling system to partition the geometric representation of a three-dimensional part into a series of simpler sub-parts the union of which replicates the original part in a maimer that introduces a minimal number of new surfaces in each sub-part and in total. This approach uses the existing analytic surfaces that define the part geometry to partition the part and selects a partition from a quality metric based on the number of trimmed surfaces of the part being partitioned and the candidate sub-parts. This approach greatly reduces the complexity of any downstream solid modeling applications that perform combinatorial surface operations on the geometric representation of the series of sub-parts to analyze physical characteristics such as radiation, mechanical, optical, thermal, structural or biological of the original part.

Abstract: A recursive binary splitting and recombination procedure coupled with a specially tailored genetic algorithm provides a solution to the general binary minimization problem with much lower run times than other methods. A minor modification to the procedure solves a variant of the binary minimization problem using an alternate operator logic that is crucial to solving certain combinatorial geometry problems.

Abstract: The descriptions of higher order complex geometry in CAD systems are fundamentally different from and seemingly incompatible with the surface based combinatorial geometry (SBCG) format for describing the same geometry in the context of general ray-tracing applications such as radiation transport. A computer implemented process translates the high order complex geometry embodied in CAD software to the SBCG format. The translation process is comprised of a set of lower-level algorithms that operate on two data sets which are commonly available from commercial CAD software systems. The first data set is a list of trimmed surfaces which make up a given part. These data are typically available from one of the standard geometry representations such as IGES, STEP, or ACIS, at least one of which is supported by each of the major CAD systems (e.g. ProEngineer). The second data set is nodal data: an appropriately dense grouping of point coordinates, designated as either inside or outside the part.

Abstract: A recursive binary splitting and recombination procedure coupled with a specially tailored genetic algorithm provides a solution to the general binary minimization problem with much lower run times than other methods. A minor modification to the procedure solves a variant of the binary minimization problem using an alternate operator logic that is crucial to solving certain combinatorial geometry problems.

Abstract: The descriptions of higher order complex geometry in CAD systems are fundamentally different from and seemingly incompatible with the surface based combinatorial geometry (SBCG) format for describing the same geometry in the context of general ray-tracing applications such as radiation transport. A computer implemented process translates the high order complex geometry embodied in CAD software to the SBCG format. The translation process is comprised of a set of lower-level algorithms that operate on two data sets which are commonly available from commercial CAD software systems. The first data set is a list of trimmed surfaces which make up a given part. These data are typically available from one of the standard geometry representations such as IGES, STEP, or ACIS, at least one of which is supported by each of the major CAD systems (e.g. ProEngineer). The second data set is nodal data: an appropriately dense grouping of point coordinates, designated as either inside or outside the part.