SU(4) Theory for Spin Systems with Orbital Degeneracy

The isotropic limit of spin systems with orbital degeneracy is shown to have global SU(4) symmetry. On many 2D lattices, the ground state does not posses long range order, which may explain the observed spin liquid properties of $LiNiO_2$. In the SU(4) Neel ordered state, spin-spin correlations can be antiferromagneitc between two neighboring sites with parallel magnetic moments.Comment: 11 pages, 2 figures. submitted to PR

Predictive protocol of flocks with small-world connection pattern

By introducing a predictive mechanism with small-world connections, we propose a new motion protocol for self-driven flocks. The small-world connections are implemented by randomly adding long-range interactions from the leader to a few distant agents, namely pseudo-leaders. The leader can directly affect the pseudo-leaders, thereby influencing all the other agents through them efficiently. Moreover, these pseudo-leaders are able to predict the leader's motion several steps ahead and use this information in decision making towards coherent flocking with more stable formation. It is shown that drastic improvement can be achieved in terms of both the consensus performance and the communication cost. From the industrial engineering point of view, the current protocol allows for a significant improvement in the cohesion and rigidity of the formation at a fairly low cost of adding a few long-range links embedded with predictive capabilities. Significantly, this work uncovers an important feature of flocks that predictive capability and long-range links can compensate for the insufficiency of each other. These conclusions are valid for both the attractive/repulsive swarm model and the Vicsek model.Comment: 10 pages, 12 figure

Needed for completion of the human genome: hypothesis driven experiments and biologically realistic mathematical models

With the sponsorship of ``Fundacio La Caixa'' we met in Barcelona, November 21st and 22nd, to analyze the reasons why, after the completion of the human genome sequence, the identification all protein coding genes and their variants remains a distant goal. Here we report on our discussions and summarize some of the major challenges that need to be overcome in order to complete the human gene catalog.Comment: Report and discussion resulting from the `Fundacio La Caixa' gene finding meeting held November 21 and 22 2003 in Barcelon