Graph-theoretic strengths of contextuality

Cabello-Severini-Winter and Abramsky-Hardy (building on the framework of Abramsky-Brandenburger) both provide classes of Bell and contextuality inequalities for very general experimental scenarios using vastly different mathematical techniques. We review both approaches, carefully detail the links between them, and give simple, graph-theoretic methods for finding inequality-free proofs of nonlocality and contextuality and for finding states exhibiting strong nonlocality and/or contextuality. Finally, we apply these methods to concrete examples in stabilizer quantum mechanics relevant to understanding contextuality as a resource in quantum computation.Comment: 13 pages; significantly rewritte

A Unified Algebraic Framework for Fuzzy Image Compression and Mathematical Morphology

In this paper we show how certain techniques of image processing, having different scopes, can be joined together under a common "algebraic roof"

State complexity of catenation combined with a boolean operation: a unified approach

In this paper we study the state complexity of catenation combined with symmetric difference. First, an upper bound is computed using some combinatoric tools. Then, this bound is shown to be tight by giving a witness for it. Moreover, we relate this work with the study of state complexity for two other combinations: catenation with union and catenation with intersection. And we extract a unified approach which allows to obtain the state complexity of any combination involving catenation and a binary boolean operation

Maximally-localized Wannier Functions in Antiferromagnetic MnO within the FLAPW Formalism

We have calculated the maximally-localized Wannier functions of MnO in its antiferromagnetic (AFM) rhombohedral unit cell, which contains two formula units. Electron Bloch functions are obtained with the linearized augmented plane-wave method within both the LSD and the LSD+U schemes. The thirteen uppermost occupied spin-up bands correspond in a pure ionic scheme to the five Mn 3d orbitals at the Mn_1 (spin-up) site, and the four O 2s/2p orbitals at each of the O_1 and O_2 sites. Maximal localization identifies uniquely four Wannier functions for each O, which are trigonally-distorted sp^3-like orbitals. They display a weak covalent bonding between O 2s/2p states and minority-spin d states of Mn_2, which is absent in a fully ionic picture. This bonding is the fingerprint of the interaction responsible for the AFM ordering, and its strength depends on the one-electron scheme being used. The five Mn Wannier functions are centered on the Mn_1 site, and are atomic orbitals modified by the crystal field. They are not uniquely defined by the criterion of maximal localization and we choose them as the linear combinations which diagonalize the r^2 operator, so that they display the D_3d symmetry of the Mn_1 site.Comment: 11 pages, 6 PostScript figures. Uses Revtex4. Hi-res figures available from the author

Finding the grey in the blue : transparency and disclosure in teaching

Police services have traditionally valued the ability to work without ongoing public scrutiny of their investigations and operations. They can very reasonably cite the need to avoid alerting criminals to police activities that might result in their arrest and charging with offences, the need to protect police and witness safety, and the frequent need to act swiftly and decisively without obtaining special approval from relevant authorities or endorsement from public opinion. This necessary lack of disclosure concerning many police operations has often extended into a general lack of transparency regarding police activities and expenditures, to the extent that, in many countries, the police services are regarded as unaccountable and unconcerned with how public opinion perceives them. In such a climate, police corruption and arbitrary exercise of police power flourishes. This paper addresses the creation of a policing environment radically different from this through the introduction of transparency into policing in the UK and the consequent revelation of layers of grey documentation and data. The paper makes use of official documentation and case studies of selected British police forces to show how the culture of policing is being changed. The principles of open government, scrutiny, and disclosure with a view to establishing accountability, are in the process of becoming institutionalised in the UK right across government, local government, other ‘public authorities’ and the business and nongovernmental organisation (NGO) sectors. The UK Human Rights Act 1998 sets the context, and a legal framework for this transparency is provided by the Freedom of Information Act 2000 and, to some extent, the Public Interest Disclosure Act 1998. The press and civil society are consistently using these mechanisms to call those with political and economic power to account. It has become apparent, even in sectors formerly as concerned with avoiding openness as the police service, that pro-active disclosure is the best way to meet public expectations. Police services now respond as a matter of course to freedom of information requests, organise a range of meetings to provide information and answer questions (from local officers’ meetings with community groups through to major budget consultative meetings with citizens’ panels), and participate in public and semi-public enquiries into aspects of the success or failure of police programmes and operations. The case studies in this paper will explore the opinions of key players in this process and draw attention to the grey information that is becoming available as a consequence

Binary morphological shape-based interpolation applied to 3-D tooth reconstruction

In this paper we propose an interpolation algorithm using a mathematical morphology morphing approach. The aim of this algorithm is to reconstruct the $n$-dimensional object from a group of (n-1)-dimensional sets representing sections of that object. The morphing transformation modifies pairs of consecutive sets such that they approach in shape and size. The interpolated set is achieved when the two consecutive sets are made idempotent by the morphing transformation. We prove the convergence of the morphological morphing. The entire object is modeled by successively interpolating a certain number of intermediary sets between each two consecutive given sets. We apply the interpolation algorithm for 3-D tooth reconstruction