Consider a convex set S = {x ∈ D : G(x) o 0} where G(x) is a symmetric matrix whose every entry is a polynomial or rational function, D ⊆ R is a domain on which G(x) is defined, and G(x) o 0 means G(x) is positive semidefinite. The set S is called semidefinite representable if it equals the projection of a higher dimensional set which is defined by a linear matrix inequality (LMI). This paper s...

Nonnegative Matrix Factorization (NMF) has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be partsbased in the human brain. However, when labeled and unlabeled images are sampled from different distributions, they may be quantized into different basis vector space and represented in different coding ...

In this paper we begin by describing two currently used methods for evaluating phylogenetic trees, one proposed by Fitch and Margoliash 5] and the other proposed by Saitou and Nei 7]. Both methods are heuristic in the sense that not all possible trees are tested to ensure that the best solution has been reached. We develop a matrix representation of unrooted binary trees. The problem of evaluat...

Let (I be a column of the fft x /I matrix M and A a set of its columns. We say that A implies a iff M contains no two rows equal in A but different in a. It is easy IO see that if Y,~,(A) denotes . the columns implied by A, than :/,,,(A) is a closure operation. We say that M represents this closure operation. s(:/ ) is the minimum number of the rows of the matrices representing a given closure ...

We investigate how the matrix representation of SU(N) algebra approaches that of the Poisson algebra in the large N limit. In the adjoint representation, the (N2 − 1)× (N2 − 1) matrices of the SU(N) generators go to those of the Poisson algebra in the large N limit. However, it is not the case for the N × N matrices in the fundamental representation.

Hibbett, D. S., and M. J. Donoghue. 1998. Integrating phylogenetic analysis and classification in fungi. Mycologia 90:347–356. Hibbett, D. S., and Thorn, R.G. 2001. Basidiomycota: Homobasidiomycetes. Pages 121–168 in The Mycota VII, systematics and evolution, Part B (D. J. McLaughlin, E. G. McLaughlin, and P. A. Lemke, eds.) Springer Verlag, Berlin. Hopple, J. S., Jr., and R. Vilgalys. 1994. Ph...

Algebraic operations on matrices can be interpreted geometrically if one considers coefficients of matrices as coordinates of vectors. However, our geometrical intuition suggests that vectors “exist” in their own right irrespective of their coordinates. After all, the same vector may have different coordinates in different coordinate systems. This means that the link between vectorial quantitie...

In this paper it is investigated how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs). Therefore it is useful to extend the known method of matrix representation by using these sequences instead of ONBs for these application areas. We will give ba...

A recently developed semantic theory explains the relationship between knowledge and its representation in connectionist systems. The theory requires a mathematical model of the brain, i.e. a natural neural network. The goal of this project is to conceptualize and lay the groundwork for the development of an adjacency matrix representation of the human and rat brains. Recent data from neuroscie...