Now showing items 41-60 of 75

    • Why is Symmetry So Hard? 

      Maurer (2011-05-13)
      The problem of detecting virtually any type of symmetry is shown to be co-NP-complete. We start with totally symmetric functions, then extend the result to partially symmetric functions, then to more general cofactor ...
    • Extending Symmetric Variable-Pair Transitivities Using State-Space Transformations 

      Maurer, Peter (2011-05-13)
      Two-cofactor relations and their associated symmetry types have been studied for many years. While ordinary symmetries are simply transitive permitting them to be combined into clusters of variables, other types of symmetries ...
    • Bootstrapping Bipartite Graphs Consisting of Edges Based on Ontology Terms Occurring in Scientific Abstract 

      Morillo, Daniel (2011-05-13)
      The Ontological Discovery Environment (ODE) provides an efficient structure for storage of gene and pheno- type relations. The relations can be represented by a bipartite graph, where the gene and phenotype items can be ...
    • MovieOracle System 

      Yao, Yao (2011-09-13)
      The detailed design document covers the basic theory, related technique, and implementation details of the MovieOracle system. It first provides a high-level system overview. Then it discusses the usage of Twitter API, ...
    • The Subgroups of S4 in Cycle Form 

      Maurer, Peter M. (2012-01-19)
      This technical report lists all subgroups of S4, the symmetric group of degree 4. Subgroups are listed in cycle form using the integers 0, 1, 2, and 3.
    • The Subgroups of S3 in Cycle Form 

      Maurer, Peter M. (2012-01-19)
      This technical report lists all subgroups of S3 in cycle form.
    • The General Linear Group of GF(2)^4 

      Maurer, Peter M. (2012-01-19)
      This technical report lists all 4x4 matrices over GF(2). Each matrix is listed along with its order and its inverse. At the end is a summary of the number of matrices belonging to each order.
    • Anti-Symmetry and Logic Simulation 

      Maurer, Peter M. (2012-01-19)
      Like ordinary symmetries, anti-symmetries are defined in terms of relations between function cofactors. For ordinary symmetries, two cofactors must be equal, for anti-symmetries two cofactors must be complements of ...
    • The General Linear Group of GF(2)^3 

      Maurer, Peter M. (2012-01-19)
      This technical report lists all 3x3 matrices over GF(2). Each matrix is listed along with its order and its inverse. At the end is a summary of the number of matrices belonging to each order.
    • The Subgroups of S5 in Cycle Form 

      Maurer, Peter M. (2012-01-19)
      This technical report lists all subgroups of S5 in cycle form, using the integers 0-4.
    • The Subgroups of S6 in Cycle Form 

      Maurer, Peter M. (2012-01-19)
      This technical report lists all subgroups of S6 in cycle form using the integers 0-5.
    • Class 9 4x4 Faithful Representations of S4 over GF(2) 

      Maurer, Peter M. (2013-09-20)
      There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 9.
    • Conjugates of the Standard Representation of S3 in 3x3 matrices 

      Maurer, Peter M. (2013-09-20)
      This is a list of the 28 conjugates of the standard representation of S3 in 3x3 matrices.
    • The Class 5 4x4 Faithful Representations of S4 over GF(2) 

      Maurer, Peter M. (2013-09-20)
      There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 5.
    • Primitive Polynomials for the Field GF(2): Degree 2 through Degree 16 

      Maurer, Peter M. (2013-09-20)
      This report lists the primitive polynomials over GF(2) of degree 2 through 16. These polynomials were generated using a new matrix-based technique I invented.
    • The Class 10 4x4 Faithful Representations of S4 over GF(2) 

      Maurer, Peter M. (2013-09-20)
      There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 10. (There is no class 6, so the classes are ...
    • The Conjugacy Classes of 3x3 and 4x4 Matrices Over GF(2) 

      Maurer, Peter M. (2013-09-20)
      The general linear groups over GF(2) have an intricate and interesting structure. This report does some preliminary work in examining the structure of two of these groups by giving the conjugacy classes of 3x3 and 4x4 ...
    • Generator Pairs for all 4x4 GF(2) Representations of S4 

      Maurer, Peter M. (2013-09-20)
      There are nine conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices. This report gives generator matrices for one group in each class. These generator pairs allow each of the ...
    • The Class 4 4x4 Faithful Representations of S4 over GF(2) 

      Maurer, Peter M. (2013-09-20)
      There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 4.
    • The Class 7 4x4 Faithful Representations of S4 over GF(2) 

      Maurer, Peter M. (2013-09-20)
      There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 7.