On the polar decomposition of right linear operators in quaternionic Hilbert spaces

In this article we prove the existence of the polar decomposition for densely defined closed right linear operators in quaternionic Hilbert spaces: If $T$ is a densely defined closed right linear operator in a quaternionic Hilbert space $H$, then there exists a partial isometry $U_{0}$ such that $T = U_{0}|T|$. In fact $U_{0}$ is unique if $N(U_{0}) = N(T)$. In particular, if $H$ is separable and $U$ is a partial isometry with $T = U|T|$, then we prove that $U = U_{0}$ if and only if either $N(T) = \{0\}$ or $R(T)^{\bot} = \{0\}$.Comment: 17 page

Countable Random Sets: Uniqueness in Law and Constructiveness

The first part of this article deals with theorems on uniqueness in law for \sigma-finite and constructive countable random sets, which in contrast to the usual assumptions may have points of accumulation. We discuss and compare two approaches on uniqueness theorems: First, the study of generators for \sigma-fields used in this context and, secondly, the analysis of hitting functions. The last section of this paper deals with the notion of constructiveness. We will prove a measurable selection theorem and a decomposition theorem for constructive countable random sets, and study constructive countable random sets with independent increments.Comment: Published in Journal of Theoretical Probability (http://www.springerlink.com/content/0894-9840/). The final publication is available at http://www.springerlink.co

Tensor products of subspace lattices and rank one density

We show that, if $M$ is a subspace lattice with the property that the rank one subspace of its operator algebra is weak* dense, $L$ is a commutative subspace lattice and $P$ is the lattice of all projections on a separable infinite dimensional Hilbert space, then the lattice $L\otimes M\otimes P$ is reflexive. If $M$ is moreover an atomic Boolean subspace lattice while $L$ is any subspace lattice, we provide a concrete lattice theoretic description of $L\otimes M$ in terms of projection valued functions defined on the set of atoms of $M$. As a consequence, we show that the Lattice Tensor Product Formula holds for \Alg M and any other reflexive operator algebra and give several further corollaries of these results.Comment: 15 page

Quantum Homodyne Tomography as an Informationally Complete Positive Operator Valued Measure

We define a positive operator valued measure $E$ on $[0,2\pi]\times R$ describing the measurement of randomly sampled quadratures in quantum homodyne tomography, and we study its probabilistic properties. Moreover, we give a mathematical analysis of the relation between the description of a state in terms of $E$ and the description provided by its Wigner transform.Comment: 9 page

There exist non orthogonal quantum measurements that are perfectly repeatable

We show that, contrarily to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors--the customary paradigm of "observable". Nonorthogonal repeatability, however, occurs only for infinite dimensions. We also show that when a non orthogonal repeatable measurement is performed, the measured system retains some "memory" of the number of times that the measurement has been performed.Comment: 4 pages, 1 figure, revtex4, minor change

Detection and prevention of financial abuse against elders

This article is made available through the Brunel Open Access Publishing Fund. Copyright @ The Authors. This article is published under the Creative Commons Attribution (CC BY 3.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/ by/3.0/legalcode.Purpose – This paper reports on banking and finance professionals' decision making in the context of elder financial abuse. The aim was to identify the case features that influence when abuse is identified and when action is taken. Design/methodology/approach – Banking and finance professionals (n=70) were shown 35 financial abuse case scenarios and were asked to judge how certain they were that the older person was being abused and the likelihood of taking action. Findings – Three case features significantly influenced certainty of financial abuse: the nature of the financial problem presented, the older person's level of mental capacity and who was in charge of the client's money. In cases where the older person was more confused and forgetful, there was increased suspicion that financial abuse was taking place. Finance professionals were less certain that financial abuse was occurring if the older person was in charge of his or her own finances. Originality/value – The research findings have been used to develop freely available online training resources to promote professionals' decision making capacity (www.elderfinancialabuse.co.uk). The resources have been advocated for use by Building Societies Association as well as CIFAS, the UK's Fraud Prevention Service.The research reported here was funded by the UK cross council New Dynamicsof Ageing Programme, ESRC Reference No. RES-352-25-0026, with Mary L.M. Gilhooly asPrincipal Investigator. Web-based training tools, developed from the research findings, weresubsequently funded by the ESRC follow-on fund ES/J001155/1 with Priscilla A. Harries asPrincipal Investigator

Treatment outcome of supraglottoplasty vs. wait-and-see policy in patients with laryngomalacia

In most cases, laryngomalacia presents as a mild disease, and the symptoms resolve after wait-and-see policy. Up to 20 % of patients present with severe laryngomalacia and may require surgery (i.e. supraglottoplasty); however, the indication for surgery is not firmly established yet. The goal of this study is to determine whether supraglottoplasty results in a better outcome than wait-and-see and to investigate how different comorbidities influence outcome. A retrospective study of pediatric cases of in a tertiary referral center was performed. Photo and video documentation was available and revised in all cases. Electronic and paper charts were reviewed for the following variables: gender, sex, gestational age, birth weight, symptoms, comorbidity, date of endoscopy, severity and type of laryngomalacia, treatment modality and technique and follow-up data and a total 89 patients were included. Supraglottoplasty was found to lead to significantly faster complete improvement of laryngomalacia than wait-and-see policy (5 weeks vs. 29, p = 0.026). Synchronous airway lesions (SALs) were present in 40.4 % of patients and were associated with prolonged symptoms of laryngomalacia (38.5 weeks vs. 14.5, p = 0.043). Supraglottoplasty is safe and effective in treatment of severe laryngomalacia. SALs and comorbidities are frequently found in patients with laryngomalacia and are responsible for longer onset of complaints

Cholesterol efflux pathways, inflammation, and atherosclerosis

Plasma levels of high-density lipoprotein (HDL) inversely correlate with the incidence of cardiovascular diseases (CVD). The causal relationship between plasma HDL-cholesterol levels and CVD has been called into question by Mendelian randomization studies and the majority of clinical trials not showing any benefit of plasma HDL-cholesterol raising drugs on CVD. Nonetheless, recent Mendelian randomization studies including an increased number of CVD cases compared to earlier studies have confirmed that HDL-cholesterol levels and CVD are causally linked. Moreover, several studies in large population cohorts have shown that the cholesterol efflux capacity of HDL inversely correlates with CVD. Cholesterol efflux pathways exert anti-inflammatory and antiatherogenic effects by suppressing proliferation of hematopoietic stem and progenitor cells, and inflammation and inflammasome activation in macrophages. Cholesterol efflux pathways also suppress the accumulation of cholesteryl esters in macrophages, i.e. macrophage foam cell formation. Recent single-cell RNASeq studies on atherosclerotic plaques have suggested that macrophage foam cells have lower expression of inflammatory genes than non-foam cells, probably reflecting liver X receptor activation, upregulation of ATP Binding Cassette A1 and G1 cholesterol transporters and suppression of inflammation. However, when these pathways are defective lesional foam cells may become pro-inflammatory

Multipartite entanglement in fermionic systems via a geometric measure

We study multipartite entanglement in a system consisting of indistinguishable fermions. Specifically, we have proposed a geometric entanglement measure for N spin-1/2 fermions distributed over 2L modes (single particle states). The measure is defined on the 2L qubit space isomorphic to the Fock space for 2L single particle states. This entanglement measure is defined for a given partition of 2L modes containing m >= 2 subsets. Thus this measure applies to m <= 2L partite fermionic system where L is any finite number, giving the number of sites. The Hilbert spaces associated with these subsets may have different dimensions. Further, we have defined the local quantum operations with respect to a given partition of modes. This definition is generic and unifies different ways of dividing a fermionic system into subsystems. We have shown, using a representative case, that the geometric measure is invariant under local unitaries corresponding to a given partition. We explicitly demonstrate the use of the measure to calculate multipartite entanglement in some correlated electron systems. To the best of our knowledge, there is no usable entanglement measure of m > 3 partite fermionic systems in the literature, so that this is the first measure of multipartite entanglement for fermionic systems going beyond the bipartite and tripartite cases.Comment: 25 pages, 8 figure