Complete positivity of the map from a basis to its dual basis

The dual of a matrix ordered space has a natural matrix ordering that makes the dual space matrix ordered as well. The purpose of these notes is to give a condition that describes when the linear map taking a basis of the n by n matrices to its dual basis is a complete order isomorphism and complete co-order isomorphism. In the case of the standard matrix units this map is a complete order isomorphism and this is a restatement of the correspondence between completely positive maps and the Choi matrix. However, we exhibit natural orthonormal bases for the matrices such that this map is an order isomorphism, but not a complete order isomorphism. Some bases yield complete co-order isomorphisms. Included among such bases is the Pauli basis and tensor products of the Pauli basis. Consequently, when the Pauli basis is used in place of the the matrix unit basis, the analogue of Choi's theorem is a characterization of completely co-positive maps

On the relationship between sigma models and spin chains

We consider the two-dimensional $\rm O(3)$ non-linear sigma model with topological term using a lattice regularization introduced by Shankar and Read [Nucl.Phys. B336 (1990), 457], that is suitable for studying the strong coupling regime. When this lattice model is quantized, the coefficient $\theta$ of the topological term is quantized as $\theta=2\pi s$, with $s$ integer or half-integer. We study in detail the relationship between the low energy behaviour of this theory and the one-dimensional spin-$s$ Heisenberg model. We generalize the analysis to sigma models with other symmetries.Comment: To appear in Int. J. MOd. Phys.

Development of prototype abstraction and exemplar memorization

We present a connectionist model of concept learning that integrates prototype and exemplar effects and reconciles apparently conflicting findings on the development of these effects. Using sibling-descendant cascade-correlation networks, we found that prototype effects were more prominent at the beginning of training and decreased with further training. In contrast, exemplar effects steadily increased with learning. Both kinds of effects were also influenced by category structure. Well-differentiated categories encouraged prototype abstraction while poorly structured categories promoted example memorization.Irina Baetu and Thomas R. Shult

Spin transition in Gd3_3N@C80_{80}, detected by low-temperature on-chip SQUID technique

We present a magnetic study of the Gd$_3$N@C$_{80}$ molecule, consisting of a Gd-trimer via a Nitrogen atom, encapsulated in a C$_{80}$ cage. This molecular system can be an efficient contrast agent for Magnetic Resonance Imaging (MRI) applications. We used a low-temperature technique able to detect small magnetic signals by placing the sample in the vicinity of an on-chip SQUID. The technique implemented at NHMFL has the particularity to operate in high magnetic fields of up to 7 T. The Gd$_3$N@C$_{80}$ shows a paramagnetic behavior and we find a spin transition of the Gd$_3$N structure at 1.2 K. We perform quantum mechanical simulations, which indicate that one of the Gd ions changes from a $^8S_{7/2}$ state ($L=0, S=7/2$) to a $^7F_{6}$ state ($L=S=3, J=6$), likely due to a charge transfer between the C$_{80}$ cage and the ion

MOBSTER -- VII. Using light curves to infer magnetic and rotational properties of stars with centrifugal magnetospheres

Early-type B stars with strong magnetic fields and rapid rotation form centrifugal magnetospheres (CMs), as the relatively weak stellar wind becomes magnetically confined and centrifugally supported above the Kepler co-rotation radius. CM plasma is concentrated at and above the Kepler co-rotation radius at the intersection between the rotation and magnetic field axis. Stellar rotation can cause these clouds of material to intersect the viewer's line-of-sight, leading to photometric eclipses. However, for stars with strong ($\sim 10\,{\rm kG}$) magnetic fields and rapid rotation, CMs can become optically thick enough for emission to occur via electron scattering. Using high-precision space photometry from a sample of stars with strong H$\alpha$ emission, we apply simulated light curves from the Rigidly Rotating Magnetosphere model to directly infer magnetic and rotational properties of these stars. By comparing the values inferred from photometric modelling to those independently determined by spectropolarimetry, we find that magnetic obliquity angle $\beta$, viewer inclination $i$ and critical rotation fraction $W$ can be approximately recovered for 3 of the 4 stars studied here. However, there are large discrepancies between the optical depth at the Kepler radius $\tau_{\rm K}$ expected from magnetometry, and the values required to match the observations. We show that $\tau_{\rm K}$ of order unity is needed to reasonably match the light curve morphology of our sample stars.Comment: 15 pages, 8 figures. Accepted for publication in MNRA

Global Citizenship Education: A Critical Introduction to Key Concepts and Debates

Global Citizenship Education explores key ideas and issues within this field, placing them firmly within local, national and global dimensions. Including examples and case studies from across the world, the authors draw on ideas, experiences and histories within and beyond 'the West' to contribute to multifaceted perspectives on global citizenship education

Infant cortex responds to other humans from shortly after birth

A significant feature of the adult human brain is its ability to selectively process information about conspecifics. Much debate has centred on whether this specialization is primarily a result of phylogenetic adaptation, or whether the brain acquires expertise in processing social stimuli as a result of its being born into an intensely social environment. Here we study the haemodynamic response in cortical areas of newborns (1–5 days old) while they passively viewed dynamic human or mechanical action videos. We observed activation selective to a dynamic face stimulus over bilateral posterior temporal cortex, but no activation in response to a moving human arm. This selective activation to the social stimulus correlated with age in hours over the first few days post partum. Thus, even very limited experience of face-to-face interaction with other humans may be sufficient to elicit social stimulus activation of relevant cortical regions

Risks, Health Consequences, and Response Challenges for Small-Island-Based Populations: Observations From the 2017 Atlantic Hurricane Season

The intensely active 2017 Atlantic basin hurricane season provided an opportunity to examine how climate drivers, including warming oceans and rising seas, exacerbated tropical cyclone hazards. The season also highlighted the unique vulnerabilities of populations residing on Small Island Developing States (SIDS) to the catastrophic potential of these storms. During 2017, 22 of the 29 Caribbean SIDS were affected by at least one named storm, and multiple SIDS experienced extreme damage. This paper aims to review the multiplicity of storm impacts on Caribbean SIDS throughout the 2017 season, to explicate the influences of climate drivers on storm formation and intensity, to explore the propensity of SIDS to sustain severe damage and prolonged disruption of essential services, to document the spectrum of public health consequences, and to delineate the daunting hurdles that challenged emergency response and recovery operations for island-based, disaster-affected populations