Bi-partite entanglement entropy in integrable models with backscattering

In this paper we generalise the main result of a recent work by J. L. Cardy and the present authors concerning the bi-partite entanglement entropy between a connected region and its complement. There the expression of the leading order correction to saturation in the large distance regime was obtained for integrable quantum field theories possessing diagonal scattering matrices. It was observed to depend only on the mass spectrum of the model and not on the specific structure of the diagonal scattering matrix. Here we extend that result to integrable models with backscattering (i.e. with non-diagonal scattering matrices). We use again the replica method, which connects the entanglement entropy to partition functions on Riemann surfaces with two branch points. Our main conclusion is that the mentioned infrared correction takes exactly the same form for theories with and without backscattering. In order to give further support to this result, we provide a detailed analysis in the sine-Gordon model in the coupling regime in which no bound states (breathers) occur. As a consequence, we obtain the leading correction to the sine-Gordon partition function on a Riemann surface in the large distance regime. Observations are made concerning the limit of large number of sheets.Comment: 22 pages, 2 figure

Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz

We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin-1/2 Heisenberg chains using the algebraic Bethe ansatz. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices which act on ${\bar {\mathscr H}}$, the tensor product of auxiliary spaces. By changing the basis in ${\bar {\mathscr H}}$, we derive explicit finite-dimensional representations for the matrices. These matrices are the same as those appearing in the recently proposed matrix product ansatz by Alcaraz and Lazo [Alcaraz F C and Lazo M J 2006 {\it J. Phys. A: Math. Gen.} \textbf{39} 11335.] apart from normalization factors. We also discuss the close relation between the matrix product representation of the Bethe eigenstates and the six-vertex model with domain wall boundary conditions [Korepin V E 1982 {\it Commun. Math. Phys.}, \textbf{86} 391.] and show that the change of basis corresponds to a mapping from the six-vertex model to the five-vertex model.Comment: 24 pages; minor typos are correcte

Metric trees of generalized roundness one

Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify some large classes of countable metric trees that have generalized roundness precisely one. At the outset we consider spherically symmetric trees endowed with the usual combinatorial metric (SSTs). Using a simple geometric argument we show how to determine decent upper bounds on the generalized roundness of finite SSTs that depend only on the downward degree sequence of the tree in question. By considering limits it follows that if the downward degree sequence $(d_{0}, d_{1}, d_{2}...)$ of a SST $(T,\rho)$ satisfies $|\{j \, | \, d_{j} > 1 \}| = \aleph_{0}$, then $(T,\rho)$ has generalized roundness one. Included among the trees that satisfy this condition are all complete $n$-ary trees of depth $\infty$ ($n \geq 2$), all $k$-regular trees ($k \geq 3$) and inductive limits of Cantor trees. The remainder of the paper deals with two classes of countable metric trees of generalized roundness one whose members are not, in general, spherically symmetric. The first such class of trees are merely required to spread out at a sufficient rate (with a restriction on the number of leaves) and the second such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table

Higher particle form factors of branch point twist fields in integrable quantum field theories

In this paper we compute higher particle form factors of branch point twist fields. These fields were first described in the context of massive 1+1-dimensional integrable quantum field theories and their correlation functions are related to the bi-partite entanglement entropy. We find analytic expressions for some form factors and check those expressions for consistency, mainly by evaluating the conformal dimension of the corresponding twist field in the underlying conformal field theory. We find that solutions to the form factor equations are not unique so that various techniques need to be used to identify those corresponding to the branch point twist field we are interested in. The models for which we carry out our study are characterized by staircase patterns of various physical quantities as functions of the energy scale. As the latter is varied, the beta-function associated to these theories comes close to vanishing at several points between the deep infrared and deep ultraviolet regimes. In other words, renormalisation group flows approach the vicinity of various critical points before ultimately reaching the ultraviolet fixed point. This feature provides an optimal way of checking the consistency of higher particle form factor solutions, as the changes on the conformal dimension of the twist field at various energy scales can only be accounted for by considering higher particle form factor contributions to the expansion of certain correlation functions.Comment: 25 pages, 4 figures; v2 contains small correction

Large-scale Nonlinear Variable Selection via Kernel Random Features

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the first kernel-based variable selection method applicable to large datasets. It sidesteps the typical poor scaling properties of kernel methods by mapping the inputs into a relatively low-dimensional space of random features. The algorithm discovers the variables relevant for the regression task together with learning the prediction model through learning the appropriate nonlinear random feature maps. We demonstrate the outstanding performance of our method on a set of large-scale synthetic and real datasets.Comment: Final version for proceedings of ECML/PKDD 201

Activity profile of top-class association football referees in relation to fitness test performance and match standard

The aim of this study was to examine the kinematic activity profiles, cardiovascular responses and physical fitness of top-class football referees (n=11) during the FIFA Confederations Cup 2005. Computerised match-analyses (n=9) were performed with a two-dimensional photogrammetric video system, and the cardiovascular demand imposed on the referees (n=12) was measured using heart rate recordings. Total distance covered was 10,218, s=643 m of which 3531, s=510 m was covered at high intensities (>3.6 m.s(-1)). Both total distance covered (r2=0.59; P=0.02) and high-intensity activities (r2=0.44; P=0.05) were related to the distance covered by the ball in the same match. The referees ran at high speed 37% further (P=0.01) in the actual tournament than during under-17 top-level officiating. After the 5-min interval during which high-speed running peaked, in the following 5 min the performance was reduced by 19% (P=0.01) in relation to the mean of the game. Mean heart rate was 161, s=9 b.min(-1) (86, s=3% of maximal heart rate (HRmax)). Mean heart rate (expressed as percentage of HRmax) was related in part (r2=0.36; P5 m.s(-1)) best describes the physical performance of referees; (3) heart rate recording can be a useful tool to determine the most intense periods of a match and (4) the new fitness tests adopted by FIFA were poor predictors of match activities

Bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories

This paper is a review of the main results obtained in a series of papers involving the present authors and their collaborator J L Cardy over the last 2 years. In our work, we have developed and applied a new approach for the computation of the bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories. In most of our work we have also considered these theories to be integrable. Our approach combines two main ingredients: the 'replica trick' and form factors for integrable models and more generally for massive quantum field theory. Our basic idea for combining fruitfully these two ingredients is that of the branch-point twist field. By the replica trick, we obtained an alternative way of expressing the entanglement entropy as a function of the correlation functions of branch-point twist fields. On the other hand, a generalization of the form factor program has allowed us to study, and in integrable cases to obtain exact expressions for, form factors of such twist fields. By the usual decomposition of correlation functions in an infinite series involving form factors, we obtained exact results for the infrared behaviours of the bi-partite entanglement entropy, and studied both its infrared and ultraviolet behaviours for different kinds of models: with and without boundaries and backscattering, at and out of integrability

Bat IFITM3 restriction depends on S-palmitoylation and a polymorphic site within the CD225 domain

Host interferon-induced transmembrane proteins (IFITMs) are broad-spectrum antiviral restriction factors. Of these, IFITM3 potently inhibits viruses that enter cells through acidic endosomes, many of which are zoonotic and emerging viruses with bats (order Chiroptera) as their natural hosts. We previously demonstrated that microbat IFITM3 is antiviral. Here, we show that bat IFITMs are characterized by strong adaptive evolution and identify a highly variable and functionally important site-codon 70-within the conserved CD225 domain of IFITMs. Mutation of this residue in microbat IFITM3 impairs restriction of representatives of four different virus families that enter cells via endosomes. This mutant shows altered subcellular localization and reduced S-palmitoylation, a phenotype copied by mutation of conserved cysteine residues in microbat IFITM3. Furthermore, we show that microbat IFITM3 is S-palmitoylated on cysteine residues C71, C72, and C105, mutation of each cysteine individually impairs virus restriction, and a triple C71A-C72A-C105A mutant loses all restriction activity, concomitant with subcellular re-localization of microbat IFITM3 to Golgi-associated sites. Thus, we propose that S-palmitoylation is critical for Chiropteran IFITM3 function and identify a key molecular determinant of IFITM3 S-palmitoylation