A Generalized Circle Theorem on Zeros of Partition Function at Asymmetric First Order Transitions

We present a generalized circle theorem which includes the Lee-Yang theorem for symmetric transitions as a special case. It is found that zeros of the partition function can be written in terms of discontinuities in the derivatives of the free energy. For asymmetric transitions, the locus of the zeros is tangent to the unit circle at the positive real axis in the thermodynamic limit. For finite-size systems, they lie off the unit circle if the partition functions of the two phases are added up with unequal prefactors. This conclusion is substantiated by explicit calculation of zeros of the partition function for the Blume-Capel model near and at the triple line at low temperatures.Comment: 10 pages, RevTeX. To be published in PRL. 3 Figures will be sent upon reques

Exact Zeros of the Partition Function for a Continuum System with Double Gaussian Peaks

We calculate the exact zeros of the partition function for a continuum system where the probability distribution for the order parameter is given by two asymmetric Gaussian peaks. When the positions of the two peaks coincide, the two separate loci of zeros which used to give first-order transition touch each other, with density of zeros vanishing at the contact point on the positive real axis. Instead of the second-order transition of Ehrenfast classification as one might naively expect, one finds a critical behavior in this limit.Comment: 13 pages, 6 figures, revtex, minor changes in fig.2, to be published in Physical Review

Renormalization Effects in a Dilute Bose Gas

The low-density expansion for a homogeneous interacting Bose gas at zero temperature can be formulated as an expansion in powers of $\sqrt{\rho a^3}$, where $\rho$ is the number density and $a$ is the S-wave scattering length. Logarithms of $\rho a^3$ appear in the coefficients of the expansion. We show that these logarithms are determined by the renormalization properties of the effective field theory that describes the scattering of atoms at zero density. The leading logarithm is determined by the renormalization of the pointlike $3 \to 3$ scattering amplitude.Comment: 10 pages, 1 postscript figure, LaTe

Mesenchymal stem cell secretes microparticles enriched in pre-microRNAs

10.1093/nar/gkp857Nucleic Acids Research381215-22

Distribution and density of the partition function zeros for the diamond-decorated Ising model

Exact renormalization map of temperature between two successive decorated lattices is given, and the distribution of the partition function zeros in the complex temperature plane is obtained for any decoration-level. The rule governing the variation of the distribution pattern as the decoration-level changes is given. The densities of the zeros for the first two decoration-levels are calculated explicitly, and the qualitative features about the densities of higher decoration-levels are given by conjecture. The Julia set associated with the renormalization map is contained in the distribution of the zeros in the limit of infinite decoration level, and the formation of the Julia set in the course of increasing the decoration-level is given in terms of the variations of the zero density.Comment: 8 pages,8figure

Uncertainty in mapped geological boundaries held by a national geological survey: eliciting the geologists' tacit error model

It is generally accepted that geological line work, such as mapped boundaries, are uncertain for various reasons. It is difficult to quantify this uncertainty directly, because the investigation of error in a boundary at a single location may be costly and time consuming, and many such observations are needed to estimate an uncertainty model with confidence. However, it is recognized across many disciplines that experts generally have a tacit model of the uncertainty of information that they produce (interpretations, diagnoses, etc.) and formal methods exist to extract this model in usable form by elicitation. In this paper we report a trial in which uncertainty models for geological boundaries mapped by geologists of the British Geological Survey (BGS) in six geological scenarios were elicited from a group of five experienced BGS geologists. In five cases a consensus distribution was obtained, which reflected both the initial individually elicited distribution and a structured process of group discussion in which individuals revised their opinions. In a sixth case a consensus was not reached. This concerned a boundary between superficial deposits where the geometry of the contact is hard to visualize. The trial showed that the geologists' tacit model of uncertainty in mapped boundaries reflects factors in addition to the cartographic error usually treated by buffering line work or in written guidance on its application. It suggests that further application of elicitation, to scenarios at an appropriate level of generalization, could be useful to provide working error models for the application and interpretation of line work

Nonperturbative Effects from the Resummation of Perturbation Theory

Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect we argue that the nonperturbative effect associated with the perturbation theory should have a branch cut only along the positive real axis in the complex coupling plane. The component in the weak coupling expansion of the nonperturbative amplitude, which usually includes the leading term in the weak coupling expansion, that gives rise to the branch cut can be calculated in principle from the perturbation theory combined with some exactly calculable properties of the nonperturbative effect. The realization of this mechanism is demonstrated in the double well potential and the two-dimensional O(N) nonlinear sigma model. In these models the leading term in weak coupling of the nonperturbative effect can be obtained with good accuracy from the first terms of the perturbation theory. Applying this mechanism to the infrared renormalon induced nonperturbative effect in QCD, we suggest some of the QCD condensate effects can be calculated in principle from the perturbation theory.Comment: 21 Pages, 1 Figure; To appear in Phys Rev

Zeros of the Partition Function and Pseudospinodals in Long-Range Ising Models

The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find the spinodal is associated with the zeros of the partition function in four-dimensional complex temperature/magnetic field space. The zeros approach the real temperature/magnetic field plane as the range of interaction increases.Comment: 20 pages, 9 figures, accepted to PR

Comparison of Genomes of Three Xanthomonas oryzae Bacteriophages

<p>Abstract</p> <p>Background</p> <p>Xp10 and OP1 are phages of <it>Xanthomonas oryzae </it>pv. oryzae (Xoo), the causative agent of bacterial leaf blight in rice plants, which were isolated in 1967 in Taiwan and in 1954 in Japan, respectively. We recently isolated the Xoo phage Xop411.</p> <p>Results</p> <p>The linear Xop411 genome (44,520 bp, 58 ORFs) sequenced here is 147 bp longer than that of Xp10 (60 ORFs) and 735 bp longer than that of OP1 (59 ORFs). The G+C contents of OP1 (51%) and Xop411 and Xp10 (52% each) are less than that of the host (65%). The 9-bp 3'-overhangs (5'-GGACAGTCT-3') in Xop411 and Xp10 are absent from OP1. More of the deduced Xop411 proteins share higher degrees of identity with Xp10 than with OP1 proteins, while the right end of the genomes of Xp10 and OP1, containing all predicted promoters, share stronger homology. Xop411, Xp10, and OP1 contain 8, 7, and 6 freestanding HNH endonuclease genes, respectively. These genes can be classified into five groups depending on their possession of the HNH domain (HNN or HNH type) and/or AP2 domain in intact or truncated forms. While the HNN-AP2 type endonuclease genes dispersed in the genome, the HNH type endonuclease genes, each with a unique copy, were located within the same genome context. Mass spectrometry and N-terminal sequencing showed nine Xop411 coat proteins, among which three were identified, six were assigned as coat proteins (4) and conserved phage proteins (2) in Xp10. The major coat protein, in which only the N-terminal methionine is removed, appears to exist in oligomeric forms containing 2 to 6 subunits. The three phages exhibit different patterns of domain duplication in the N-terminus of the tail fiber, which are involved in determination of the host range. Many short repeated sequences are present in and around the duplicated domains.</p> <p>Conclusion</p> <p>Geographical separation may have confined lateral gene transfer among the Xoo phages. The HNN-AP2 type endonucleases were more likely to transfer their genes randomly in the genome and may degenerate after successful transmission. Some repeated sequences may be involved in duplication/loss of the domains in the tail fiber genes.</p