Rational Approximate Symmetries of KdV Equation

We construct one-parameter deformation of the Dorfman Hamiltonian operator for the Riemann hierarchy using the quasi-Miura transformation from topological field theory. In this way, one can get the approximately rational symmetries of KdV equation and then investigate its bi-Hamiltonian structure.Comment: 14 pages, no figure

Collapsed 2-Dimensional Polymers on a Cylinder

Single partially confined collapsed polymers are studied in two dimensions. They are described by self-avoiding random walks with nearest-neighbour attractions below the $\Theta$-point, on the surface of an infinitely long cylinder. For the simulations we employ the pruned-enriched-Rosenbluth method (PERM). The same model had previously been studied for free polymers (infinite lattice, no boundaries) and for polymers on finite lattices with periodic boundary conditions. We verify the previous estimates of bulk densities, bulk free energies, and surface tensions. We find that the free energy of a polymer with fixed length $N$ has, for $N\to \infty$, a minimum at a finite cylinder radius $R^*$ which diverges as $T\to T_\theta$. Furthermore, the surface tension vanishes roughly as $(T_\theta-T)^\alpha$ for $T\to T_\theta$ with $\alpha\approx 1.7$. The density in the interior of a globule scales as $(T_\theta-T)^\beta$ with $\beta \approx 0.32$.Comment: 4 pages, 8 figure

A review of Monte Carlo simulations of polymers with PERM

In this review, we describe applications of the pruned-enriched Rosenbluth method (PERM), a sequential Monte Carlo algorithm with resampling, to various problems in polymer physics. PERM produces samples according to any given prescribed weight distribution, by growing configurations step by step with controlled bias, and correcting "bad" configurations by "population control". The latter is implemented, in contrast to other population based algorithms like e.g. genetic algorithms, by depth-first recursion which avoids storing all members of the population at the same time in computer memory. The problems we discuss all concern single polymers (with one exception), but under various conditions: Homopolymers in good solvents and at the $\Theta$ point, semi-stiff polymers, polymers in confining geometries, stretched polymers undergoing a forced globule-linear transition, star polymers, bottle brushes, lattice animals as a model for randomly branched polymers, DNA melting, and finally -- as the only system at low temperatures, lattice heteropolymers as simple models for protein folding. PERM is for some of these problems the method of choice, but it can also fail. We discuss how to recognize when a result is reliable, and we discuss also some types of bias that can be crucial in guiding the growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011

"Minus c" Symmetry in Classical and Quantum Theories

It is shown that the transformations of the charge conjugation in classical electrodynamics and in quantum theory can be interpreted as the consequences of the symmetry of Maxwell and Dirac equations with respect to the inversion of the speed of light: c to -c; t to t; (x,y,z) to (x,y,z), where c is the speed of light; t is the time; x, y, z are the spatial variables. The elements of physical interpretation are given.Comment: 12 pages, LaTeX, Poster at the Fifth International Conference on Squeezed States and Uncertainty Relations, May 27-31, 1997, Balatonfured, Hungar

Li non-stoichiometry and crystal growth of untwinned 1D quantum spin system Lix Cu2 O2

Floating-zone growth of untwinned single crystal of Li_xCu_2O_2 with high Li content of x ~ 0.99 is reported. Li content of Li_xCu_2O_2 has been determined accurately through combined iodometric titration and thermogravimetric methods, which also ruled out the speculation of chemical disorder between Li and Cu ions. The morphology and physical properties of single crystals obtained from slowing-cooling (SL) and floating-zone (FZ) methods are compared. The floating-zone growth under Ar/O_2=7:1 gas mixture at 0.64 MPa produces large area of untwinned crystal with highest Li content, which has the lowest helimagnetic ordering temperature ~19K in the Li_xCu_2O_2 system.Comment: 4 pages, 3 figure

Multi-Throat Brane Inflation

We present a scenario where brane inflation arises more generically. We start with D3 and anti-D3-branes at the infrared ends of two different throats. This setup is a natural consequence of the assumption that in the beginning we have a multi-throat string compactification with many wandering anti-D3-branes. A long period of inflation is triggered when D3-branes slowly exit the highly warped infrared region, under a potential generically arising from the moduli stabilization. In this scenario, the usual slow-roll conditions are not required, and a large warping is allowed to incorporate the Randall-Sundrum model.Comment: 11 pages; v3: minor revision, PRD versio

Cosmological Rescaling through Warped Space

We discuss a scenario where at least part of the homogeneity on a brane world can be directly related to the hierarchy problem through warped space. We study the dynamics of an anti-D3-brane moving toward the infrared cut-off of a warped background. After a region described by the DBI action, the self-energy of the anti-D3-brane will dominate over the background. Then the world-volume scale of the anti-D3-brane is no longer comoving with the background geometry. After it settles down in the infrared end, the world-volume inhomogeneity will appear, to a Poincare observer, to be stretched by an exponentially large ratio. This ratio is close to that of the hierarchy problem between the gravitational and electroweak scales.Comment: 12 pages, 2 figures; v2, PRD version, comments and references adde

Genetic variants in ARID5B and CEBPE are childhood ALL susceptibility loci in Hispanics.

Recent genome-wide studies conducted in European Whites have identified novel susceptibility genes for childhood acute lymphoblastic leukemia (ALL). We sought to examine whether these loci are susceptibility genes among Hispanics, whose reported incidence of childhood ALL is the highest of all ethnic groups in California, and whether their effects differ between Hispanics and non-Hispanic Whites (NHWs). We genotyped 13 variants in these genes among 706 Hispanic (300 cases, 406 controls) and 594 NHW (225 cases, 369 controls) participants in a matched population-based case-control study in California. We found significant associations for the five studied ARID5B variants in both Hispanics (p values of 1.0 × 10(-9) to 0.004) and NHWs (p values of 2.2 × 10(-6) to 0.018). Risk estimates were in the same direction in both groups (ORs of 1.53-1.99 and 1.37-1.84, respectively) and strengthened when restricted to B-cell precursor high-hyperdiploid ALL (>50 chromosomes; ORs of 2.21-3.22 and 1.67-2.71, respectively). Similar results were observed for the single CEBPE variant. Hispanics and NHWs exhibited different susceptibility loci at CDKN2A. Although IKZF1 loci showed significant susceptibility effects among NHWs (p < 1 × 10(-5)), their effects among Hispanics were in the same direction but nonsignificant, despite similar minor allele frequencies. Future studies should examine whether the observed effects vary by environmental, immunological, or lifestyle factors

Fisher Renormalization for Logarithmic Corrections

For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee problem at their upper critical dimensions, where predictions for logarithmic corrections are made.Comment: 10 pages, no figures. Version 2 has added reference