Analysis of two-player quantum games in an EPR setting using geometric algebra

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of Clifford geometric algebra (GA). In this setting, the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, which is then obtained as proper subset of the corresponding quantum game. As examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt when played in the EPR type setting.Comment: 20 pages, no figure, revise

N-player quantum games in an EPR setting

The $N$-player quantum game is analyzed in the context of an Einstein-Podolsky-Rosen (EPR) experiment. In this setting, a player's strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players' strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find the relations for the probability distribution for $N$-qubit GHZ and W-type states, subject to general measurement directions, from which the expressions for the mixed Nash equilibrium and the payoffs are determined. Players' payoffs are then defined with linear functions so that common two-player games can be easily extended to the $N$-player case and permit analytic expressions for the Nash equilibrium. As a specific example, we solve the Prisoners' Dilemma game for general $N \ge 2$. We find a new property for the game that for an even number of players the payoffs at the Nash equilibrium are equal, whereas for an odd number of players the cooperating players receive higher payoffs.Comment: 26 pages, 2 figure

Analyzing three-player quantum games in an EPR type setup

We use the formalism of Clifford Geometric Algebra (GA) to develop an analysis of quantum versions of three-player non-cooperative games. The quantum games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting. In this setting, the players' strategy sets remain identical to the ones in the mixed-strategy version of the classical game that is obtained as a proper subset of the corresponding quantum game. Using GA we investigate the outcome of a realization of the game by players sharing GHZ state, W state, and a mixture of GHZ and W states. As a specific example, we study the game of three-player Prisoners' Dilemma.Comment: 21 pages, 3 figure

Theory of Cylindrical Tubules and Helical Ribbons of Chiral Lipid Membranes

We present a general theory for the equilibrium structure of cylindrical tubules and helical ribbons of chiral lipid membranes. This theory is based on a continuum elastic free energy that permits variations in the direction of molecular tilt and in the curvature of the membrane. The theory shows that the formation of tubules and helical ribbons is driven by the chirality of the membrane. Tubules have a first-order transition from a uniform state to a helically modulated state, with periodic stripes in the tilt direction and ripples in the curvature. Helical ribbons can be stable structures, or they can be unstable intermediate states in the formation of tubules.Comment: 43 pages, including 12 postscript figures, uses REVTeX 3.0 and epsf.st

The field theory of symmetrical layered electrolytic systems and the thermal Casimir effect

We present a general extension of a field-theoretic approach developed in earlier papers to the calculation of the free energy of symmetrically layered electrolytic systems which is based on the Sine-Gordon field theory for the Coulomb gas. The method is to construct the partition function in terms of the Feynman evolution kernel in the Euclidean time variable associated with the coordinate normal to the surfaces defining the layered structure. The theory is applicable to cylindrical systems and its development is motivated by the possibility that a static van der Waals or thermal Casimir force could provide an attractive force stabilising a dielectric tube formed from a lipid bilayer, an example of which are t-tubules occurring in certain muscle cells. In this context, we apply the theory to the calculation of the thermal Casimir effect for a dielectric tube of radius $R$ and thickness $\delta$ formed from such a membrane in water. In a grand canonical approach we find that the leading contribution to the Casimir energy behaves like $-k_BTL\kappa_C/R$ which gives rise to an attractive force which tends to contract the tube radius. We find that $\kappa_C \sim 0.3$ for the case of typical lipid membrane t-tubules. We conclude that except in the case of a very soft membrane this force is insufficient to stabilise such tubes against the bending stress which tend to increase the radius. We briefly discuss the role of lipid membrane reservoir implicit in the approach and whether its nature in biological systems may possibly lead to a stabilising mechanism for such lipid tubes.Comment: 28 pages, 2 figures, LaTe

Interstellar cloud structure: The statistics of centroid velocities

The investigation of the statistical properties of maps of line centroids has been used for almost 50 years, but there is still no general agreement on their interpretation. We try to quantify which properties of underlying turbulent velocity fields can be derived from centroid velocity maps, and we test conditions under which the scaling behaviour of the centroid velocities matches the scaling of the three-dimensional velocity field. Using fractal cloud models we study systematically the relation between three-dimensional density and velocity fields and the statistical properties of the produced line centroid maps. We put special attention to cases with large density fluctuations resembling supersonic interstellar turbulence. Starting from the Delta-variance analysis we derive a new tool to compute the scaling behaviour of the three-dimensional velocity field from observed intensity and centroid velocity maps. We provide two criteria to decide whether the information from the centroid velocities directly reflects the properties of the underlying velocity field. Applying these criteria allows to understand the different results found so far in the literature on the interpretation of the statistics of velocity centroids. A new iteration scheme can be used to derive the three-dimensional velocity scaling from centroid velocity maps for arbitrary density and velocity fields, but it requires an accurate knowledge of the average density of the considered interstellar cloud.Comment: Accepted for publication in Astronomy & Astrophysic

Estimation of cold plasma outflow during geomagnetic storms

Low-energy ions of ionospheric origin constitute a significant contributor to the magnetospheric plasma population. Measuring cold ions is difficult though. Observations have to be done at sufficiently high altitudes and typically in regions of space where spacecraft attain a positive charge due to solar illumination. Cold ions are therefore shielded from the satellite particle detectors. Furthermore, spacecraft can only cover key regions of ion outflow during segments of their orbit, so additional complications arise if continuous longtime observations, such as during a geomagnetic storm, are needed. In this paper we suggest a new approach, based on a combination of synoptic observations and a novel technique to estimate the flux and total outflow during the various phases of geomagnetic storms. Our results indicate large variations in both outflow rates and transport throughout the storm. Prior to the storm main phase, outflow rates are moderate, and the cold ions are mainly emanating from moderately sized polar cap regions. Throughout the main phase of the storm, outflow rates increase and the polar cap source regions expand. Furthermore, faster transport, resulting from enhanced convection, leads to a much larger supply of cold ions to the near-Earth region during geomagnetic storms. ©2015. The Authors

'You were quiet - I did all the marching': Research processes involved in hearing the voices of South Asian girls

This article is available open access through the publisher’s website at the link below. Copyright @ 2011 A B Academic Publishers.This article provides insights into the outcomes of reflection following two interview approaches used to explore narratives of the lived, individual experiences of South-Asian girls living in West London. In attempting to illuminate and re-present the cultural experiences as told by these girls, the choice of interview approach became critical in allowing the voices to be effectively heard (Rogers, 2005). This article therefore considers how a semi-structured interview approach offered valuable insights into the girls' experiences but became constraining for both researcher and participant in unveiling the complexity and depth of their lives. These constraints emerged through reflection by both participants and researcher. As a result of reflexivity during the research process, the researcher moved towards the use of research conversations during the second phase of the study. Ultimately the study revealed how the girls felt empowered by the opportunity to narrate their individual experiences and tell of their lives. In narrating their reflections on being part of the research, there was a clear recognition that the process facilitated the articulation of new voices and ‘multi-voicedness’ (Moen, 2006

Creative learning conversations: producing living dialogic spaces

publication-status: Publishedtypes: ArticleBackground ‘Creative learning conversations’, are methodological devices developed in two co-participative qualitative research projects exploring creativity and educational futures at the University of Exeter in England. Sources of evidence Framed by Critical Theory, the projects, one on dance education partnership, the other on student voice and transformation, sought to open space between creativity and performativity to initiate emancipatory educational change. This was undertaken over the course of five years in English primary and secondary schools, prioritising humanising, wise creativity (Chappell, 2008; Craft, 2008). Purpose This paper re-analyses data and methodological processes to characterise and theorise creative learning conversations in terms of social spatiality and dialogue. The characteristics are: partiality, emancipation, working from the ‘bottom up’, participation, debate and difference, openness to action, and embodied and verbalised idea exchange. Main argument This re-analysis theoretically adapts Bronfenbrenner’s (1979) ecological model to situate layered engagement. Utilising Lefebvre’s (1991) conceptualisation of Lived space and Bakhtin’s (1984) work on open-ended dialogue, the paper theorises creative learning conversations as producing living dialogic spaces. Conclusions Creative learning conversations are a way of contributing to change which moves us towards an education future fit for the twenty-first century. From a living dialogic space perspective a creative learning conversation is the ongoing process without forced closure of those in the roles of University academic, teachers, artists, students co-participatively researching and developing knowledge of their ‘lived space’ together. Given traditional lethargy in the educational system as a whole commitment to changing education for better futures demands active involvement in living dialogic space, where our humanity both emerges from and guides our shared learning