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

Building capacity for co-operative governance as a basis for integrated water resource managing in the Inkomati and Mvoti catchments, South Africa

South Africa’s National Water Act and National Water Resource Strategy set out an ambitious vision for Integrated Water Resources Management including a strong focus on the redistribution of water resources towards the poor and on empowering historically disadvantaged communities. To achieve this vision the Department of Water Affairs & Forestry (DWAF) has been pursuing a programme for devolving powers to 19 stakeholder-led catchment management agencies (CMAs) and more locally, transforming irrigation boards into more inclusive water user associations (WUAs), as well as creating new associations.Co-operative governance is a core principle of this programme. As well as being enshrined in South Africa’s constitution, this principle is seen as key to enabling CMAs to implement their core functions, which include co-ordinating the activities of water users and water management institutions within their water management area. For WUAs also, the principle of co-operative governance is key to building engagement between White commercial farmers and emerging Black farmers, as well as (in some cases) engaging with a wider set of stakeholder interests including local government and environmental interests.Despite a commitment to the principle of co-operative governance, individual and institutional capacity for facilitating co-operative development processes is in relatively short supply within the South African water sector. This paper describes work-in-progress to build capacity in this area, working with:• DWAF’s national Institutional Governance team• The Inkomati CMA (ICMA), the first of South Africa’s new catchment management agencies• Two irrigation boards and a number of other stakeholders in the Mvoti catchment – with a view to the development of an appropriate institutional arrangement (WUA or otherwise) for the co-operative governance of this catchment.This paper focuses on the development of an interactive approach to capacity building in each of these three sites, drawing from a broad portfolio of approaches variously described as social learning, social appraisal, or whole system development. In the Inkomati we have worked primarily with the whole system approach known as Future Search, whereas in the Mvoti we have used the U-process and social appraisal as guiding metaphors and design principles.This paper describes some of our achievements, challenges and reflections to date, and argues that the interactive approaches we have been taking are better suited to the implementation of DWAF’s institutional reform processes than the more established, top-down approaches, which involve issuing guidance, supported by training programmes. The paper concludes with a discussion of the implications for scaling up these types of approaches across the South African water system as a whole, and for the practice of integrated water resource management.Keywords: adaptive IWRM, catchment management agencies, cooperative governance, dialogue, interactive capacity building, social learning, water user association

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

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

Parameter identification problems in the modelling of cell motility

We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference between the computed and observed data are proposed and the parameter identification problem is formulated as a minimisation problem of nonlinear least squares type. A Levenberg–Marquardt based optimisation method is applied to the solution of the minimisation problem and the details of the implementation are discussed. A number of numerical experiments are presented which illustrate the robustness of the algorithm to parameter identification in the presence of large deformations and noisy data and parameter identification in three dimensional models of cell motility. An application to experimental data is also presented in which we seek to identify parameters in a model for the monopolar growth of fission yeast cells using experimental imaging data. Our numerical tests allow us to compare the method with the two different formulations of the objective functional and we conclude that the results with both objective functionals seem to agree

The politics of in/visibility: carving out queer space in Ul'yanovsk

<p>In spite of a growing interest within sexualities studies in the concept of queer space (Oswin 2008), existing literature focuses almost exclusively on its most visible and territorialised forms, such as the gay scene, thus privileging Western metropolitan areas as hubs of queer consumer culture (Binnie 2004). While the literature has emphasised the political significance of queer space as a site of resistance to hegemonic gender and sexual norms, it has again predominantly focused on overt claims to public space embodied in Pride events, neglecting other less open forms of resistance.</p><p> This article contributes new insights to current debates about the construction and meaning of queer space by considering how city space is appropriated by an informal queer network in Ul’ianovsk. The group routinely occupied very public locations meeting and socialising on the street or in mainstream cafés in central Ul’ianovsk, although claims to these spaces as queer were mostly contingent, precarious or invisible to outsiders. The article considers how provincial location affects tactics used to carve out communal space, foregrounding the importance of local context and collective agency in shaping specific forms of resistance, and questioning ethnocentric assumptions about the empowering potential of visibility.</p&gt

Sensory professionals’ perspective on the possibilities of using facial expression analysis in sensory and consumer research

The increase in digitalization, software applications, and computing power has widened the variety of tools with which to collect and analyze sensory data. As these changes continue to take place, examining new skills required among sensory professionals is needed. The aim with this study was to answer the following questions: (a) How did sensory professionals perceive the opportunities to utilize facial expression analysis in sensory evaluation work? (b) What skills did the sensory professionals describe they needed when utilizing facial expression analysis? Twenty-two sensory professionals from various food companies and universities were interviewed by using semistructural thematic interviews to map development intentions from facial expression recognition data as well as to describe the established skills that were needed. Participants' facial expressions were first elicited by an odor sample during a sensory evaluation task. The evaluation was video recorded to characterize a facial expression software response (FaceReader (TM)). The participants were interviewed regarding their opinions of the data analysis the software produced. The study findings demonstrate how using facial expression analysis contains personal and field-specific perspectives. Recognizability, associativity, reflectivity, reliability, and suitability were perceived as a personal perspective. From the field-specific perspective, professionals considered the received data valuable only if they had skills to interpret and utilize it. There is a need for an increase in training not only in IT, mathematics, statistics, and problem-solving, but also in skills related to self-management and ethical responsibility.Peer reviewe

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

Entanglement in Many-Body Systems

The recent interest in aspects common to quantum information and condensed matter has prompted a prosperous activity at the border of these disciplines that were far distant until few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, the properties of the entanglement in many-body systems. We discuss the zero and finite temperature properties of entanglement in interacting spin, fermionic and bosonic model systems. Both bipartite and multipartite entanglement will be considered. At equilibrium we emphasize on how entanglement is connected to the phase diagram of the underlying model. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium we discuss how to generate and manipulate entangled states by means of many-body Hamiltonians.Comment: 61 pages, 29 figure