40 research outputs found
Uniqueness and order in sequential effect algebras
A sequential effect algebra (SEA) is an effect algebra on which a sequential
product is defined. We present examples of effect algebras that admit a unique,
many and no sequential product. Some general theorems concerning unique
sequential products are proved. We discuss sequentially ordered SEA's in which
the order is completely determined by the sequential product. It is
demonstrated that intervals in a sequential ordered SEA admit a sequential
product
Compression Bases in Unital Groups
We study unital groups with a distinguished family of compressions called a
compression base. A motivating example is the partially ordered additive group
of a von Neumann algebra with all Naimark compressions as the compression base.Comment: 8 page
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
The Lattice and Simplex Structure of States on Pseudo Effect Algebras
We study states, measures, and signed measures on pseudo effect algebras with
some kind of the Riesz Decomposition Property, (RDP). We show that the set of
all Jordan signed measures is always an Abelian Dedekind complete -group.
Therefore, the state space of the pseudo effect algebra with (RDP) is either
empty or a nonempty Choquet simplex or even a Bauer simplex. This will allow
represent states on pseudo effect algebras by standard integrals
Type-Decomposition of a Pseudo-Effect Algebra
The theory of direct decomposition of a centrally orthocomplete effect
algebra into direct summands of various types utilizes the notion of a
type-determining (TD) set. A pseudo-effect algebra (PEA) is a (possibly)
noncommutative version of an effect algebra. In this article we develop the
basic theory of centrally orthocomplete PEAs, generalize the notion of a TD set
to PEAs, and show that TD sets induce decompositions of centrally orthocomplete
PEAs into direct summands.Comment: 18 page
Information-theoretic principle entails orthomodularity of a lattice
Quantum logical axiomatic systems for quantum theory usually include a
postulate that a lattice under consideration is orthomodular. We propose a
derivation of orthomodularity from an information-theoretic axiom. This
provides conceptual clarity and removes a long-standing puzzle about the
meaning of orthomodularity.Comment: Version prior to published, with slight modification
On the lattice structure of probability spaces in quantum mechanics
Let C be the set of all possible quantum states. We study the convex subsets
of C with attention focused on the lattice theoretical structure of these
convex subsets and, as a result, find a framework capable of unifying several
aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent
principle. We also encounter links with entanglement witnesses, which leads to
a new separability criteria expressed in lattice language. We also provide an
extension of a separability criteria based on convex polytopes to the infinite
dimensional case and show that it reveals interesting facets concerning the
geometrical structure of the convex subsets. It is seen that the above
mentioned framework is also capable of generalization to any statistical theory
via the so-called convex operational models' approach. In particular, we show
how to extend the geometrical structure underlying entanglement to any
statistical model, an extension which may be useful for studying correlations
in different generalizations of quantum mechanics.Comment: arXiv admin note: substantial text overlap with arXiv:1008.416
Kochen-Specker Vectors
We give a constructive and exhaustive definition of Kochen-Specker (KS)
vectors in a Hilbert space of any dimension as well as of all the remaining
vectors of the space. KS vectors are elements of any set of orthonormal states,
i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to
assign 1s and 0s in such a way that no two mutually orthogonal vectors from the
set are both assigned 1 and that not all mutually orthogonal vectors are
assigned 0. Our constructive definition of such KS vectors is based on
algorithms that generate MMP diagrams corresponding to blocks of orthogonal
vectors in R^n, on algorithms that single out those diagrams on which algebraic
0-1 states cannot be defined, and on algorithms that solve nonlinear equations
describing the orthogonalities of the vectors by means of statistically
polynomially complex interval analysis and self-teaching programs. The
algorithms are limited neither by the number of dimensions nor by the number of
vectors. To demonstrate the power of the algorithms, all 4-dim KS vector
systems containing up to 24 vectors were generated and described, all 3-dim
vector systems containing up to 30 vectors were scanned, and several general
properties of KS vectors were found.Comment: 19 pages, 6 figures, title changed, introduction thoroughly
rewritten, n-dim rotation of KS vectors defined, original Kochen-Specker 192
(117) vector system translated into MMP diagram notation with a new graphical
representation, results on Tkadlec's dual diagrams added, several other new
results added, journal version: to be published in J. Phys. A, 38 (2005). Web
page: http://m3k.grad.hr/pavici