Logarithmic intertwining operators and vertex operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra $M(1)_a$, of central charge $1-12a^2$. We classify these operators in terms of {\em depth} and provide explicit constructions in all cases. Furthermore, for $a=0$ we focus on the vertex operator subalgebra L(1,0) of $M(1)_0$ and obtain logarithmic intertwining operators among indecomposable Virasoro algebra modules. In particular, we construct explicitly a family of {\em hidden} logarithmic intertwining operators, i.e., those that operate among two ordinary and one genuine logarithmic L(1,0)-module.Comment: 32 pages. To appear in CM

Aquagenic urticaria in twins

We describe the case of 18 year old twin brothers who presented to our unit with a 3 year history of aquagenic urticaria. This rare form of urticaria usually presents within an hour of contact with water. The aetiology is unknown. Most cases are sporadic but there are a small number of familial cases in the medical literature. A specific genetic mutation has not yet been found. To our knowledge, this is the first report of aquagenic urticaria in monozygotic twins, further supporting a genetic component to this disease

The influence of the strength of bone on the deformation of acetabular shells : a laboratory experiment in cadavers

Date of Acceptance: 24/08/2014 ©2015 The British Editorial Society of Bone & Joint Surgery. The authors would like to thank N. Taylor (3D Measurement Company) for his work with regard to data acquisition and processing of experimental data. We would also like to thank Dr A. Blain of Newcastle University for performing the statistical analysis The research was supported by the NIHR Newcastle Biomedical Research Centre. The authors P. Dold, M. Flohr and R. Preuss are employed by Ceramtec GmbH. Martin Bone received a salary from the joint fund. The author or one or more of the authors have received or will receive benefits for personal or professional use from a commercial party related directly or indirectly to the subject of this article. This article was primary edited by G. Scott and first proof edited by J. Scott.Peer reviewedPostprin

The Haldane-Rezayi Quantum Hall State and Conformal Field Theory

We propose field theories for the bulk and edge of a quantum Hall state in the universality class of the Haldane-Rezayi wavefunction. The bulk theory is associated with the $c=-2$ conformal field theory. The topological properties of the state, such as the quasiparticle braiding statistics and ground state degeneracy on a torus, may be deduced from this conformal field theory. The 10-fold degeneracy on a torus is explained by the existence of a logarithmic operator in the $c=-2$ theory; this operator corresponds to a novel bulk excitation in the quantum Hall state. We argue that the edge theory is the $c=1$ chiral Dirac fermion, which is related in a simple way to the $c=-2$ theory of the bulk. This theory is reformulated as a truncated version of a doublet of Dirac fermions in which the $SU(2)$ symmetry -- which corresponds to the spin-rotational symmetry of the quantum Hall system -- is manifest and non-local. We make predictions for the current-voltage characteristics for transport through point contacts.Comment: 37 pages, LaTeX. Some references added, minor changes at the end of section

Generalized twisted modules associated to general automorphisms of a vertex operator algebra

We introduce a notion of strongly C^{\times}-graded, or equivalently, C/Z-graded generalized g-twisted V-module associated to an automorphism g, not necessarily of finite order, of a vertex operator algebra. We also introduce a notion of strongly C-graded generalized g-twisted V-module if V admits an additional C-grading compatible with g. Let V=\coprod_{n\in \Z}V_{(n)} be a vertex operator algebra such that V_{(0)}=\C\one and V_{(n)}=0 for n<0 and let u be an element of V of weight 1 such that L(1)u=0. Then the exponential of 2\pi \sqrt{-1} Res_{x} Y(u, x) is an automorphism g_{u} of V. In this case, a strongly C-graded generalized g_{u}-twisted V-module is constructed from a strongly C-graded generalized V-module with a compatible action of g_{u} by modifying the vertex operator map for the generalized V-module using the exponential of the negative-power part of the vertex operator Y(u, x). In particular, we give examples of such generalized twisted modules associated to the exponentials of some screening operators on certain vertex operator algebras related to the triplet W-algebras. An important feature is that we have to work with generalized (twisted) V-modules which are doubly graded by the group C/Z or C and by generalized eigenspaces (not just eigenspaces) for L(0), and the twisted vertex operators in general involve the logarithm of the formal variable.Comment: Final version to appear in Comm. Math. Phys. 38 pages. References on triplet W-algebras added, misprints corrected, and expositions revise

The N=1 triplet vertex operator superalgebras

We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m \geq 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p \geq 2$, important in logarithmic conformal field theory. We classify irreducible SW(m)-modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible SW(m) characters. Finally, we contemplate possible connections between the category of SW(m)-modules and the category of modules for the quantum group U^{small}_q(sl_2), q=e^{\frac{2 \pi i}{2m+1}}, by focusing primarily on properties of characters and the Zhu's algebra A(SW(m)). This paper is a continuation of arXiv:0707.1857.Comment: 53 pages; v2: references added; v3: a few changes; v4: final version, to appear in CM

Conformal invariance and its breaking in a stochastic model of a fluctuating interface

Using Monte-Carlo simulations on large lattices, we study the effects of changing the parameter $u$ (the ratio of the adsorption and desorption rates) of the raise and peel model. This is a nonlocal stochastic model of a fluctuating interface. We show that for $0<u<1$ the system is massive, for $u=1$ it is massless and conformal invariant. For $u>1$ the conformal invariance is broken. The system is in a scale invariant but not conformal invariant phase. As far as we know it is the first example of a system which shows such a behavior. Moreover in the broken phase, the critical exponents vary continuously with the parameter $u$. This stays true also for the critical exponent $\tau$ which characterizes the probability distribution function of avalanches (the critical exponent $D$ staying unchanged).Comment: 22 pages and 20 figure

From boundary to bulk in logarithmic CFT

The analogue of the charge-conjugation modular invariant for rational logarithmic conformal field theories is constructed. This is done by reconstructing the bulk spectrum from a simple boundary condition (the analogue of the Cardy `identity brane'). We apply the general method to the c_1,p triplet models and reproduce the previously known bulk theory for p=2 at c=-2. For general p we verify that the resulting partition functions are modular invariant. We also construct the complete set of 2p boundary states, and confirm that the identity brane from which we started indeed exists. As a by-product we obtain a logarithmic version of the Verlinde formula for the c_1,p triplet models.Comment: 35 pages, 2 figures; v2: minor corrections, version to appear in J.Phys.

Infinite Symmetry in the Fractional Quantum Hall Effect

We have generalized recent results of Cappelli, Trugenberger and Zemba on the integer quantum Hall effect constructing explicitly a ${\cal W}_{1+\infty}$ for the fractional quantum Hall effect such that the negative modes annihilate the Laughlin wave functions. This generalization has a nice interpretation in Jain's composite fermion theory. Furthermore, for these models we have calculated the wave functions of the edge excitations viewing them as area preserving deformations of an incompressible quantum droplet, and have shown that the ${\cal W}_{1+\infty}$ is the underlying symmetry of the edge excitations in the fractional quantum Hall effect. Finally, we have applied this method to more general wave functions.Comment: 15pp. LaTeX, BONN-HE-93-2

Evaluating the removal of pigs from a group and subsequent floor space allowance on the growth performance of heavy-weight finishing pigs

Citation: Flohr, J. R., Tokach, M. D., DeRouchey, J. M., Woodworth, J. C., Goodband, R. D., & Dritz, S. S. (2016). Evaluating the removal of pigs from a group and subsequent floor space allowance on the growth performance of heavy-weight finishing pigs. Journal of Animal Science, 94(10), 4388-4400. doi:10.2527/jas2016-0407A total of 1,092 finishing pigs (initially 36.3 kg) were used in a 117-d study to evaluate the impact of initial floor space allowance and removal strategy on the growth of pigs up to 140 kg BW. There were 4 experimental treatments with 14 pens per treatment. The first treatment provided 0.91 m(2) per pig (15 pigs/pen). The other 3 treatments initially provided 0.65 m(2) per pig (21 pigs/pen) with 3 different removal strategies. The second treatment (2:2:2) removed the 2 heaviest pigs from pens on d 64, 76, and 95 when floor space allowance was predicted to be limiting. Treatment 3 (2:4) removed the 2 heaviest pigs on d 76 and the 4 heaviest pigs on d 105. Treatment 4 (6) removed the heaviest 6 pigs on d 105. All pigs remaining in pens after removals were fed to d 117. Overall (d 0 to 117), pigs initially provided 0.91 m(2) of floor space had increased (P < 0.05) ADG compared to pigs in pens on the 2: 4 or 6 removal strategy, but ADG was not different compared with pigs on the 2:2:2 removal strategy. Total BW gain per pen was greater (P < 0.05) for pens initially stocked at 0.65 m(2) compared to pens initially stocked at 0.91 m(2). Feed usage per pen was less (P < 0.05) for pens initially stocked at 0.91 m(2) compared to pens initially providing 0.65 m(2) of floor space and on removal strategies; however, feed usage per pig was greater (P < 0.05) for pigs initially stocked at 0.91 m(2) compared to pigs initially stocked at 0.65 m(2) and on removal strategies. Feed usage, on a pig or pen basis, was less (P < 0.05) for pigs on the 2: 2: 2 removal strategy compared to pigs on the 2:4 or the 6 removal strategy. Income over feed and facility cost (IOFFC) was less (P < 0.05) for pigs initially provided 0.91 m(2) compared to pigs initially provided 0.65 m(2) and on removal strategies. Also, IOFFC was less (P < 0.05) for pigs on the 2:2:2 compared to the 2:4 and 6 removal strategies. In conclusion, increasing the floor space allowance or the time points at which pigs are removed from the pen improved the growth of pigs remaining in the pen; however, IOFFC may be reduced because fewer pigs are marketed from each pen (pigs stocked at 0.91 m(2) throughout the study) or from reducing total weight produced (2:2:2 removal strategy)