The full set of cnc_n-invariant factorized SS-matrices

We use the method of the tensor product graph to construct rational (Yangian invariant) solutions of the Yang-Baxter equation in fundamental representations of $c_n$ and thence the full set of $c_n$-invariant factorized $S$-matrices. Brief comments are made on their bootstrap structure and on Belavin's scalar Yangian conserved charges.Comment: 10p

Diffraction-limited CCD imaging with faint reference stars

By selecting short exposure images taken using a CCD with negligible readout noise we obtained essentially diffraction-limited 810 nm images of faint objects using nearby reference stars brighter than I=16 at a 2.56 m telescope. The FWHM of the isoplanatic patch for the technique is found to be 50 arcseconds, providing ~20% sky coverage around suitable reference stars.Comment: 4 page letter accepted for publication in Astronomy and Astrophysic

R-matrices and Tensor Product Graph Method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.Comment: LaTex 7 pages. Contribution to the APCTP-Nankai Joint Symposium on "Lattice Statistics and Mathematical Physics", 8-10 October 2001, Tianjin, Chin

Nonlinear structures and thermodynamic instabilities in a one-dimensional lattice system

The equilibrium states of the discrete Peyrard-Bishop Hamiltonian with one end fixed are computed exactly from the two-dimensional nonlinear Morse map. These exact nonlinear structures are interpreted as domain walls (DW), interpolating between bound and unbound segments of the chain. The free energy of the DWs is calculated to leading order beyond the Gaussian approximation. Thermodynamic instabilities (e.g. DNA unzipping and/or thermal denaturation) can be understood in terms of DW formation.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Let

Community Detection as an Inference Problem

We express community detection as an inference problem of determining the most likely arrangement of communities. We then apply belief propagation and mean-field theory to this problem, and show that this leads to fast, accurate algorithms for community detection.Comment: 4 pages, 2 figure

Electronic structure of periodic curved surfaces -- topological band structure

Electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface characterized completely in terms of "navels") but represent the topology of real systems such as zeolites and negative-curvature fullerene. The band structure turns out to be primarily determined by the topology of the surface, i.e., how the wavefunction interferes on a multiply-connected surface, so that the bands are little affected by the way in which we confine the electrons on the surface (thin-slab limit or zero thickness from the outset). Another curiosity is that different minimal surfaces connected by the Bonnet transformation (such as Schwarz's P- and D-surfaces) possess one-to-one correspondence in their band energies at Brillouin zone boundaries.Comment: 6 pages, 8 figures, eps files will be sent on request to [email protected]

The Statistical Physics of Regular Low-Density Parity-Check Error-Correcting Codes

A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword which comprises Boolean sums of message bits selected by two randomly constructed sparse matrices. The similarity of these codes to Ising spin systems with random interaction makes it possible to assess their typical performance by analytical methods developed in the study of disordered systems. The typical case solutions obtained via the replica method are consistent with those obtained in simulations using belief propagation (BP) decoding. We discuss the practical implications of the results obtained and suggest a computationally efficient construction for one of the more practical configurations.Comment: 35 pages, 4 figure