It is becoming increasingly clear that the supercharacter theory of the finite group of unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions that is analogous to the partition combinatorics of the classical representation theory of the symmetric group. This paper begins by exploring a connection to the ring of symmetric functions in non-commuting variab...

This paper describes triangular risk decomposition, which provides a useful, geometric view of the relationship between the risk of a position and that of the portfolio. We review triangular decomposition for the case of the parametric, or delta-normal, Value-at-Risk (VaR), which assumes that changes in a portfolio’s value are normally distributed with mean zero. We then generalize it for the c...

Any real square matrix M can be written as M = U(I + L)S, where U is a matrix of0's, l's and l's having exactly one nonzero element in each row and column, L is a strictly lower triangular matrix, and S is a {symmetric}, positivesemidefinite matrix. The aim O f this paper is to demonstrate the utility of this easily derived fact. This is done in two ways. First, the decomposition is used to dev...

Approaches to polygonal decomposition for hierarchical image representation are described. For planar decomposition, quad trees using square and triangular neighborhoods are found to be the only feasible methods, having the same computational complexity. For grid images the choice of the appropriate tree type is determined by the grid topology. Triangular and square quad trees are appropriate f...

GPU ∗ † [Extended Abstract] Jin Hyuk Jung Department of Computer Science University of Maryland, College Park [email protected] Dianne P. O’Leary Department of Computer Science University of Maryland, College Park [email protected] ABSTRACT The rapid evolution of Graphics Processing Units (GPUs) in performance, architecture, and programmability provides computational potential beyond their prima...

Let U/K represent a connected, compact symmetric space, where θ is an involution of U that fixes K, φ : U/K → U is the geodesic Cartan embedding, and G is the complexification of U. We investigate the intersection, studied by Pickrell, of φ(U/K) with the Birkhoff decomposition of G corresponding to a θ-stable triangular, or LDU, factoriztion of Lie(G). When g ∈ φ(U/K) is generic, the factorizat...

We address the reduction to compact band forms, via unitary similarity transformations, for the solution of symmetric eigenvalue problems and the computation of the singular value decomposition (SVD). Concretely, in the first case we revisit the reduction to symmetric band form while, for the second case, we propose a similar alternative, which transforms the original matrix to (unsymmetric) ba...

This paper proposes fuzzy regression analysis with non-symmetric fuzzy coefficients. By assuming non-symmetric triangular fuzzy coefficients and applying the quadratic programming formulation, the center of the obtained fuzzy regression model attains more central tendency compared to the one with symmetric triangular fuzzy coefficients. For a data set composed of crisp inputs-fuzzy outputs, two...

An important consideration in generalised least squares problems is that the dimension of the covariance matrix V is the dimension of the data set and is large when the data set is large. Also, the problem solution can be well determined in cases where V is illconditioned or singular. Here aspects of a class of methods which factorize the design matrix while leaving V invariant, and which can b...