Abstract: A method of generating a sequence of matrix factors for a transformation matrix having a plurality of rows and columns using a computer, wherein the transformation matrix stores data values representing a wavelet transform. In a first aspect, at least one plurality of row reduction operations are applied to the transformation matrix. The sequence of matrix factors is generated from the reduced transformation matrix and the row reduction operations. A scaling factor may be removed from the transformation matrix before applying the row reduction operations, wherein the scaled transformation matrix has a determinant with a coefficient equal to 1 or ?1. In yet another aspect, the transformation matrix may have a nonzero monomial determinant and the sequence of matrix factors further includes a scaling matrix. The method may include further alternative features described herein.

Abstract: A method of generating matrix factors for a finite-dimensional linear transform using a computer. The linear transform is represented by data values stored in a linear transformation matrix having a nonzero determinant. In one aspect, a first LU-decomposition is applied to the linear transformation matrix. Four matrices are generated from the LU-decomposition, including a first permutation matrix, a second permutation matrix, a lower triangular matrix having a unit diagonal, and a first upper triangular matrix. Additional elements include a third matrix Â, a signed permutation matrix ? such that A=?Â, a permuted linear transformation matrix A?, a second upper triangular matrix U1, wherein the second upper triangular matrix satisfies the relationship Â=U1A?. The permuted linear transformation matrix is factored into a product including a lower triangular matrix L and an upper triangular matrix U. The linear transformation matrix is expressed as a product of the matrix factors.

Abstract: A method of generating matrix factors for a finite-dimensional linear transform using a computer. The linear transform is represented by data values stored in a linear transformation matrix having a nonzero determinant. In one aspect, a first LU-decomposition is applied to the linear transformation matrix. Four matrices are generated from the LU-decomposition, including a first permutation matrix, a second permutation matrix, a lower triangular matrix having a unit diagonal, and a first upper triangular matrix. Additional elements include a third matrix Â, a signed permutation matrix ? such that A=?Â, a permuted linear transformation matrix A?, a second upper triangular matrix U1, wherein the second upper triangular matrix satisfies the relationship Â=U1A?. The permuted linear transformation matrix is factored into a product including a lower triangular matrix L and an upper triangular matrix U. The linear transformation matrix is expressed as a product of the matrix factors.

Abstract: A method of generating a sequence of matrix factors for a transformation matrix having a plurality of rows and columns using a computer, wherein the transformation matrix stores data values representing a wavelet transform. In a first aspect, at least one plurality of row reduction operations are applied to the transformation matrix. The sequence of matrix factors is generated from the reduced transformation matrix and the row reduction operations. A scaling factor may be removed from the transformation matrix before applying the row reduction operations, wherein the scaled transformation matrix has a determinant with a coefficient equal to 1 or ?1. In yet another aspect, the transformation matrix may have a nonzero monomial determinant and the sequence of matrix factors further includes a scaling matrix. The method may include further alternative features described herein.

Abstract: A method for generating a first plurality of output data values and the matrix factors used to generate an approximation to an image processing transform is disclosed. The first plurality of output data values are generated by transforming a plurality of input data values using a computer and applying a modified transform stored in a modified transformation matrix to the plurality of input data values. The plurality of input data values are stored in a generated matrix, and at least one data value in this matrix is rearranged using a permutation operation and modified by applying a linear combination of the unmodified values to the at least one data value. The modified transform is an approximation to a known transform stored in a transformation matrix that is used to generate a second plurality of output data values, the first plurality of output values approximating the second plurality of output data values.

Abstract: Systems and methods are provided for characterizing a multidimensional distribution of responses from the objects in a populations subject to a perturbation. The methods enable the creation of a “degree of response” scale interpolated from non-perturbed and perturbed reference populations. The methods enables, using the interpolated degree of response scale, the quantitation of a degree of response of a test compound subject to a given level of perturbation, and enables the generation of a dose-response curve for a test compound. The methods are useful in a wide range of applications, such cellular analysis and high-content screening of compounds, as carried out in pharmaceutical research.

Abstract: A method for generating a first plurality of output data values and the matrix factors used to generate an approximation to an image processing transform is disclosed. The first plurality of output data values are generated by transforming a plurality of input data values using a computer and applying a modified transform stored in a modified transformation matrix to the plurality of input data values. The plurality of input data values are stored in a generated matrix, and at least one data value in this matrix is rearranged using a permutation operation and modified by applying a linear combination of the unmodified values to the at least one data value. The modified transform is an approximation to a known transform stored in a transformation matrix that is used to generate a second plurality of output data values, the first plurality of output values approximating the second plurality of output data values.

Abstract: An image population having a large number of attributes is processed to form a display population with a predetermined smaller number of attributes that represent the larger number of attributes. In a particular application, the color values in an image are compressed for storage in a discrete look-up table (LUT). Color space containing the LUT color values is successively subdivided into smaller volumes until a plurality of volumes are formed, each having no more than a preselected maximum number of color values. Image pixel color values can then be rapidly placed in a volume with only a relatively few LUT values from which a nearest neighbor is selected. Image color values are assigned 8 bit pointers to their closest LUT value whereby data processing requires only the 8 bit pointer value to provide 24 bit color values from the LUT.

Abstract: Livelock-free message routing is provided in a network of interconnected nodes that is flushable in time T. An input message processor generates sequences of at least N time intervals, each of duration T. An input register provides for receiving and holding each input message, where the message is assigned a priority state p during an nth one of the N time intervals. At each of the network nodes a message processor reads the assigned priority state and awards priority to messages with priority state (p-1) during an nth time interval and to messages with priority state p during an (n+1) th time interval. The messages that are awarded priority are output on an output path toward the addressed output message processor. Thus, no message remains in the network for a time longer than T.

Abstract: An image population having a large number of attributes is processed to form a display population with a predetermined smaller number of attributes which represent the larger number of attributes. In a particular application, the color values in an image are compressed for storage in a discrete lookup table (LUT) where an 8-bit data signal is enabled to form a display of 24-bit color values. The LUT is formed in a sampling and averaging process from the image color values with no requirement to define discrete Voronoi regions for color compression. Image color values are assigned 8-bit pointers to their closest LUT value whereby data processing requires only the 8-bit pointer value to provide 24-bit color values from the LUT.

Abstract: A network of interconnected processors is formed from a vertex symmetric graph selected from graphs .GAMMA..sub.d (k) with degree d, diameter k, and (d+1)!/(d-k+1)! processors for each d.gtoreq.k and .GAMMA..sub.d (k,-1) with degree 3-1, diameter k+1, and (d+1)!/(d-k+1)! processors for each d.gtoreq.k.gtoreq.4. Each processor has an address formed by one of the permutations from a predetermined sequence of letters chosen a selected number of letters at a time, and an extended address formed by appending to the address the remaining ones of the predetermined sequence of letters. A plurality of transmission channels is provided from each of the processors, where each processor has one less channel than the selected number of letters forming the sequence. Where a network .GAMMA..sub.d (k,-1) is provided, no processor has a channel connected to form an edge in a direction .delta..sub.1.