Semi-regular masas of transfinite length

In 1965 Tauer produced a countably infinite family of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor, no pair of which are conjugate by an automorphism. This was achieved by iterating the process of passing to the algebra generated by the normalisers and, for each $n\in\mathbb N$, finding masas for which this procedure terminates at the $n$-th stage. Such masas are said to have length $n$. In this paper we consider a transfinite version of this idea, giving rise to a notion of ordinal valued length. We show that all countable ordinals arise as lengths of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor. Furthermore, building on work of Jones and Popa, we obtain all possible combinations of regular inclusions of irreducible subfactors in the normalising tower.Comment: 14 page

On C*-algebras generated by pairs of q-commuting isometries

We consider the C*-algebras O_2^q and A_2^q generated, respectively, by isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| < 1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 = complex conjugate of q_2. In the second part of our paper, we discuss the complexity of the representation theory of A_2^q. We show that A_2^q is *-wild for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q in the circle.Comment: 18 pages, LaTeX2e "article" document class; submitted. V2 clarifies the relationships between the various deformation systems treate

Taylor approximations of operator functions

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.Comment: 12 page

A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself

We give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank zero and stable rank one, has a unique tracial state, and the order on projections over D is determined by traces. It also absorbs the Jiang-Su algebra Z, and in fact absorbs the 3^{\infty} UHF algebra. We can also explicitly compute the K-theory of D, namely K_0 (D) = Z[1/3] with the standard order, and K_1 (D) = 0, as well as the Cuntz semigroup of D.Comment: 16 pages; AMSLaTeX. The material on other possible K-groups for such an algebra has been moved to a separate paper (1309.4142 [math.OA]

Coherent States of the q--Canonical Commutation Relations

For the $q$-deformed canonical commutation relations $a(f)a^\dagger(g) = (1-q)\,\langle f,g\rangle{\bf1}+q\,a^\dagger(g)a(f)$ for $f,g$ in some Hilbert space ${\cal H}$ we consider representations generated from a vector $\Omega$ satisfying $a(f)\Omega=\langle f,\phi\rangle\Omega$, where $\phi\in{\cal H}$. We show that such a representation exists if and only if $\Vert\phi\Vert\leq1$. Moreover, for $\Vert\phi\Vert<1$ these representations are unitarily equivalent to the Fock representation (obtained for $\phi=0$). On the other hand representations obtained for different unit vectors $\phi$ are disjoint. We show that the universal C*-algebra for the relations has a largest proper, closed, two-sided ideal. The quotient by this ideal is a natural $q$-analogue of the Cuntz algebra (obtained for $q=0$). We discuss the Conjecture that, for $d<\infty$, this analogue should, in fact, be equal to the Cuntz algebra itself. In the limiting cases $q=\pm1$ we determine all irreducible representations of the relations, and characterize those which can be obtained via coherent states.Comment: 19 pages, Plain Te

Quantitative conversations: the importance of developing rapport in standardised interviewing

© 2014, The Author(s). When developing household surveys, much emphasis is understandably placed on developing survey instruments that can elicit accurate and comparable responses. In order to ensure that carefully crafted questions are not undermined by ‘interviewer effects’, standardised interviewing tends to be utilised in preference to conversational techniques. However, by drawing on a behaviour coding analysis of survey paradata arising from the 2012 UK Poverty and Social Exclusion Survey we show that in practice standardised survey interviewing often involves extensive unscripted conversation between the interviewer and the respondent. Whilst these interactions can enhance response accuracy, cooperation and ethicality, unscripted conversations can also be problematic in terms of survey reliability and the ethical conduct of survey interviews, as well as raising more basic epistemological questions concerning the degree of standardisation typically assumed within survey research. We conclude that better training in conversational techniques is necessary, even when applying standardised interviewing methodologies. We also draw out some theoretical implications regarding the usefulness of the qualitative–quantitative dichotomy

Pioneering the human development revolution: Analysing the trajectory of Mahbub ul Haq

Mahbub ul Haq's work to coordinate, establish and propagate the human development approach offers an example of effective leadership in promoting more ethical socio-economic development. This article reviews Pioneering the Human Development Revolution-An Intellectual Biography of Mahbub ul Haq (edited by Haq and Ponzio), and extends themes from the United Nations Intellectual History Project to examine Haq's contributions in terms of four aspects of leadership: articulating and applying values that combine depth with broad appeal; providing a fruitful and vivid way of seeing, a 'vision', that reflects the values; embodying the values and vision in workable practical proposals; and supporting and communicating the previous aspects through wide and relevant networks. It suggests that the human development approach may need to update its values and vision, including through better integration of human security thinking, if it is to retain the leadership role it acquired thanks to Haq

Publisher Correction: The genome of the stable fly, Stomoxys calcitrans, reveals potential mechanisms underlying reproduction, host interactions, and novel targets for pest control (BMC Biology, (2021), 19, 1, (41), 10.1186/s12915-021-00975-9)

Following publication of the original article [1], it was reported that the article copyright was incorrect. The correct copyright statement is: © This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2021. The original article [1] has been corrected

Numerical hydrodynamics in general relativity

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article the present update provides additional information on numerical schemes and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.Comment: 105 pages, 12 figures. The full online-readable version of this article, including several animations, will be published in Living Reviews in Relativity at http://www.livingreviews.or