We study preimages of permutations under the bubblesort operator $\mathbf{B}$. achieve a description these much more complete than what is known for complicated sorting operators $\mathbf{S}$ (stacksort) and $\mathbf{Q}$ (queuesort). describe explicitly set $\mathbf{B}$ any permutation $\pi$ from left-to-right maxima $\pi$, showing that there are $2^{k-1}$ such if $k$ number maxima. further con...

We apply the nested algebraic Bethe ansatz method to solve the eigenvalue problem for the SU(4) extension of the Hubbard model. The Hamiltonian is equivalent to the SU(4) graded permutation operator. The graded Yang-Baxter equation and the graded Quantum Inverse Scattering Method are used to obtain the eigenvalue of the SU(4) extension of the Hubbard model. PACS: 75.10.Jm, 71.10.Fd, 05.30.Fk.

We present a new lattice integrable system in one dimension of the Haldane-Shastry type. It consists of spins positioned at the static equilibrium positions of particles in a corresponding classical Calogero system and interacting through an exchange term with strength inversely proportional to the square of their distance. We achieve this by viewing the Haldane-Shastry system as a high-interac...

This paper focuses on improved edge model based on Curvelet coefficients analysis. Curvelet transform is a powerful tool for multiresolution representation of object with anisotropic edge. Curvelet coefficients contributions have been analyzed using Scale Invariant Feature Transform (SIFT), commonly used to study local structure in images. The permutation of Curvelet coefficients from original ...

A new class of positive definite functions related to colour-length function on arbitrary Coxeter group is introduced. Extensions of positive definite functions, called the Riesz-Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) group to arbitrary Coxeter group is obtained. Applications to harmonic analysis, operator spaces and noncommutative probability is presented. ...

Both direct schedule representations as well as indirect permutation-based representations in conjunction with schedule builders are successfully employed in oversubscribed scheduling research. Recent work has indicated that in some domains, searching the space of permutations as opposed to the schedule space itself can be more productive in maximizing the number of scheduled tasks. On the othe...

The choice of mutation rate is a vital factor in the success of any genetic algorithm (GA), and for permutation representations this is compounded by the availability of several alternative mutation operators. It is now well understood that there is no one "optimal choice"; rather, the situation changes per problem instance and during evolution. This paper examines whether this choice can be le...

The choice of mutation rate is a vital factor in the success of any genetic algorithm (GA), and for permutation representations this is compounded by the availability of several alternative mutation operators. It is now well understood that there is no one “optimal choice” rather the situation changes per problem instance and during evolution. This paper examines whether this choice can be left...

This is the first in a series of papers in which I investigate the orbifolds of permutation-type as candidates for new physical string systems at multiples of critical closed-string central charges. Examples include the bosonic orientation orbifolds, the bosonic permutation orbifolds and others, as well as superstring extensions. In this paper I use the extended (twisted) Virasoro algebras of t...