We investigate the statistical properties of the cross-correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the cross-correlation matrix is positively skewed and changes over time. We find that the eigenvalue distri...

Given a nonsingular n × n matrix of univariate polynomials over a field K, we give fast and deterministic algorithms to compute its determinant and its Hermite normal form. Our algorithms use Õ(nωdse) operations in K, where s is bounded from above by both the average of the degrees of the rows and that of the columns of the matrix and ω is the exponent of matrix multiplication. The soft-O notat...

We consider the problem of testing multiple quantum hypotheses {ρ 1 , . . . , ρ r }, where an arbitrary prior distribution is given and each of the r hypotheses is n copies of a quantum state. It is known that the minimal average error probability Pe decays exponentially to zero, that is, Pe = exp{−ξn+ o(n)}. However, this error exponent ξ is generally unknown, except for the case that r = 2. I...

Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional λφ model to study spontaneous breakdown of discrete Z2 symmetry numerically. We obtain the critical coupling (λ/μ 2)c = 59.89 ± 0.01 and the critical exponent β = 0.1264 ± 0.0073, which are consistent with the Monte Carlo and the exact results, respectively. The results are based on extrapolation to the continuum limi...

Transfer-matrix methods on finite-width strips with free boundary conditions are applied to lattice site animals, which provide a model for randomly branched polymers in a good solvent. By assigning a distinct fugacity to sites along the strip edges, critical properties at the special (adsorption) and ordinary transitions are assessed. The crossover exponent at the adsorption point is estimated...

A singularity on the negative fugacity axis of the hard-square lattice gas is investigated in terms of numerical diagonalization of transfer matrices. The location of the singular point z− c and the critical exponent ν are accurately determined by the phenomenological renormalization technique as −0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the...

In this paper we introduce a method that allows one to prove uniform local results for one-dimensional discrete Schrödinger operators with Sturmian potentials. We apply this method to the transfer matrices in order to study the Lyapunov exponent and the growth rate of eigenfunctions. This gives uniform vanishing of the Lyapunov exponent on the spectrum for all irrational rotation numbers. For i...

Based on Lyapunov-exponent generation and the Gram-Schimdt orthogonalization, analysis and design of some anti-controlled higher-dimensional hyperchaotic systems are investigated in this paper. First, some theoretical results for Lyapunov-exponent generating algorithms are proposed. Then, the relationship between the number of Lyapunov exponents and the number of positive real parts of the eige...

This review paper describes certain elementary methods of group theory for studying the algebraic complexity of matrix multiplication, as measured by the exponent 2 ≤ ω ≤ 3 of matrix multiplication. which is conjectured to be 2. The seed of these methods lies in two ideas of H. Cohn, C. Umans et. al., firstly, that it is possible to " realize " a matrix product via the regular algebra of a (fin...