Discovering Regression Rules with Ant Colony Optimization

The majority of Ant Colony Optimization (ACO) algorithms for data mining have dealt with classification or clustering problems. Regression remains an unexplored research area to the best of our knowledge. This paper proposes a new ACO algorithm that generates regression rules for data mining applications. The new algorithm combines components from an existing deterministic (greedy) separate and conquer algorithm—employing the same quality metrics and continuous attribute processing techniques—allowing a comparison of the two. The new algorithm has been shown to decrease the relative root mean square error when compared to the greedy algorithm. Additionally a different approach to handling continuous attributes was investigated showing further improvements were possible

Compatible orders and fermion-induced emergent symmetry in Dirac systems

We study the quantum multicritical point in a (2+1)-dimensional Dirac system between the semimetallic phase and two ordered phases that are characterized by anticommuting mass terms with $O(N_1)$ and $O(N_2)$ symmetry, respectively. Using $\epsilon$ expansion around the upper critical space-time dimension of four, we demonstrate the existence of a stable renormalization-group fixed point, enabling a direct and continuous transition between the two ordered phases directly at the multicritical point. This point is found to be characterized by an emergent $O(N_1+N_2)$ symmetry for arbitrary values of $N_1$ and $N_2$ and fermion flavor numbers $N_f$, as long as the corresponding representation of the Clifford algebra exists. Small $O(N)$-breaking perturbations near the chiral $O(N)$ fixed point are therefore irrelevant. This result can be traced back to the presence of gapless Dirac degrees of freedom at criticality, and it is in clear contrast to the purely bosonic $O(N)$ fixed point, which is stable only when $N < 3$. As a by-product, we obtain predictions for the critical behavior of the chiral $O(N)$ universality classes for arbitrary $N$ and fermion flavor number $N_f$. Implications for critical Weyl and Dirac systems in 3+1 dimensions are also briefly discussed.Comment: 5+2 pages, 1 figure, 1 tabl

Comment on ``Critical behavior of a two-species reaction-diffusion problem''

In a recent paper, de Freitas et al. [Phys. Rev. E 61, 6330 (2000)] presented simulational results for the critical exponents of the two-species reaction-diffusion system A + B -> 2B and B -> A in dimension d = 1. In particular, the correlation length exponent was found as \nu = 2.21(5) in contradiction to the exact relation \nu = 2/d. In this Comment, the symmetry arguments leading to exact critical exponents for the universality class of this reaction-diffusion system are concisely reconsidered

Correlation of eigenstates in the critical regime of quantum Hall systems

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, $\alpha_0\approx 2.28$, gives an almost complete characterization of the critical behavior of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.Comment: 17 pages, 9 Postscript figure

Fresh look at randomly branched polymers

We develop a new, dynamical field theory of isotropic randomly branched polymers, and we use this model in conjunction with the renormalization group (RG) to study several prominent problems in the physics of these polymers. Our model provides an alternative vantage point to understand the swollen phase via dimensional reduction. We reveal a hidden Becchi-Rouet-Stora (BRS) symmetry of the model that describes the collapse ($\theta$-)transition to compact polymer-conformations, and calculate the critical exponents to 2-loop order. It turns out that the long-standing 1-loop results for these exponents are not entirely correct. A runaway of the RG flow indicates that the so-called $\theta^\prime$-transition could be a fluctuation induced first order transition.Comment: 4 page