Scalar Representation and Conjugation of Set-Valued Functions

To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. Using this conjugate, weak and strong duality results are proven.Comment: arXiv admin note: substantial text overlap with arXiv:1012.435

Order recall in verbal short-term memory: The role of semantic networks

In their recent article, Acheson, MacDonald, and Postle (Journal of Experimental Psychology: Learning, Memory, and Cognition 37:44-59, 2011) made an important but controversial suggestion: They hypothesized that (a) semantic information has an effect on order information in short-term memory (STM) and (b) order recall in STM is based on the level of activation of items within the relevant lexico-semantic long-term memory (LTM) network. However, verbal STM research has typically led to the conclusion that factors such as semantic category have a large effect on the number of correctly recalled items, but little or no impact on order recall (Poirier & Saint-Aubin, Quarterly Journal of Experimental Psychology 48A:384-404, 1995; Saint-Aubin, Ouellette, & Poirier, Psychonomic Bulletin & Review 12:171-177, 2005; Tse, Memory 17:874-891, 2009). Moreover, most formal models of short-term order memory currently suggest a separate mechanism for order coding-that is, one that is separate from item representation and not associated with LTM lexico-semantic networks. Both of the experiments reported here tested the predictions that we derived from Acheson et al. The findings show that, as predicted, manipulations aiming to affect the activation of item representations significantly impacted order memory

Quantification of the performance of chaotic micromixers on the basis of finite time Lyapunov exponents

Chaotic micromixers such as the staggered herringbone mixer developed by Stroock et al. allow efficient mixing of fluids even at low Reynolds number by repeated stretching and folding of the fluid interfaces. The ability of the fluid to mix well depends on the rate at which "chaotic advection" occurs in the mixer. An optimization of mixer geometries is a non trivial task which is often performed by time consuming and expensive trial and error experiments. In this paper an algorithm is presented that applies the concept of finite-time Lyapunov exponents to obtain a quantitative measure of the chaotic advection of the flow and hence the performance of micromixers. By performing lattice Boltzmann simulations of the flow inside a mixer geometry, introducing massless and non-interacting tracer particles and following their trajectories the finite time Lyapunov exponents can be calculated. The applicability of the method is demonstrated by a comparison of the improved geometrical structure of the staggered herringbone mixer with available literature data.Comment: 9 pages, 8 figure

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Overt is no better than covert when rehearsing visuo-spatial information in working memory

In the present study, we examined whether eye movements facilitate retention of visuo-spatial information in working memory. In two experiments, participants memorised the sequence of the spatial locations of six digits across a retention interval. In some conditions, participants were free to move their eyes during the retention interval, but in others they either were required to remain fixated or were instructed to move their eyes exclusively to a selection of the memorised locations. Memory performance was no better when participants were free to move their eyes during the memory interval than when they fixated a single location. Furthermore, the results demonstrated a primacy effect in the eye movement behaviour that corresponded with the memory performance. We conclude that overt eye movements do not provide a benefit over covert attention for rehearsing visuo-spatial information in working memory

Collapse of superconductivity in a hybrid tin-graphene Josephson junction array

When a Josephson junction array is built with hybrid superconductor/metal/superconductor junctions, a quantum phase transition from a superconducting to a two-dimensional (2D) metallic ground state is predicted to happen upon increasing the junction normal state resistance. Owing to its surface-exposed 2D electron gas and its gate-tunable charge carrier density, graphene coupled to superconductors is the ideal platform to study the above-mentioned transition between ground states. Here we show that decorating graphene with a sparse and regular array of superconducting nanodisks enables to continuously gate-tune the quantum superconductor-to-metal transition of the Josephson junction array into a zero-temperature metallic state. The suppression of proximity-induced superconductivity is a direct consequence of the emergence of quantum fluctuations of the superconducting phase of the disks. Under perpendicular magnetic field, the competition between quantum fluctuations and disorder is responsible for the resilience at the lowest temperatures of a superconducting glassy state that persists above the upper critical field. Our results provide the entire phase diagram of the disorder and magnetic field-tuned transition and unveil the fundamental impact of quantum phase fluctuations in 2D superconducting systems.Comment: 25 pages, 6 figure

Boundaries of Semantic Distraction: Dominance and Lexicality Act at Retrieval

Three experiments investigated memory for semantic information with the goal of determining boundary conditions for the manifestation of semantic auditory distraction. Irrelevant speech disrupted the free recall of semantic category-exemplars to an equal degree regardless of whether the speech coincided with presentation or test phases of the task (Experiment 1) and occurred regardless of whether it comprised random words or coherent sentences (Experiment 2). The effects of background speech were greater when the irrelevant speech was semantically related to the to-be-remembered material, but only when the irrelevant words were high in output dominance (Experiment 3). The implications of these findings in relation to the processing of task material and the processing of background speech is discussed

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity which offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: 54 pages, submitted to Living Reviews in Relativit