Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given.Comment: 27 page

Non-adaptive Measurement-based Quantum Computation and Multi-party Bell Inequalities

Quantum correlations exhibit behaviour that cannot be resolved with a local hidden variable picture of the world. In quantum information, they are also used as resources for information processing tasks, such as Measurement-based Quantum Computation (MQC). In MQC, universal quantum computation can be achieved via adaptive measurements on a suitable entangled resource state. In this paper, we look at a version of MQC in which we remove the adaptivity of measurements and aim to understand what computational abilities still remain in the resource. We show that there are explicit connections between this model of computation and the question of non-classicality in quantum correlations. We demonstrate this by focussing on deterministic computation of Boolean functions, in which natural generalisations of the Greenberger-Horne-Zeilinger (GHZ) paradox emerge; we then explore probabilistic computation, via which multipartite Bell Inequalities can be defined. We use this correspondence to define families of multi-party Bell inequalities, which we show to have a number of interesting contrasting properties.Comment: 13 pages, 4 figures, final version accepted for publicatio

A review of hippocampal activation in post‐traumatic stress disorder

Post‐traumatic stress disorder (PTSD) is often characterized by deficits in memory encoding and retrieval and aberrant fear and extinction learning. The hippocampus plays a critical role in memory and contextual processing and has been implicated in intrinsic functional connectivity networks involved in self‐referential thought and memory‐related processes. This review focuses on hippocampal activation findings during memory and fear and extinction learning tasks, as well as resting state hippocampal connectivity in individuals with PTSD. A preponderance of functional neuroimaging studies to date, using memory, fear learning, and extinction tasks, report decreased or “controls comparable” hippocampal activation in individuals with PTSD, which is usually associated with poorer performance on the task imaged. Existing evidence thus raises the possibility that greater hippocampal recruitment in PTSD participants may be required for similar performance levels. Studies of resting state functional connectivity in PTSD predominantly report reduced within‐network connectivity in the default mode network (DMN), as well as greater coupling between the DMN and salience network (SN) via the hippocampus. Together, these findings suggest that deficient hippocampal activation in PTSD may be associated with poorer performance during memory, extinction recall, and fear renewal tasks. Furthermore, studies of resting state connectivity implicate the hippocampus in decreased within‐network DMN connectivity and greater coupling with SN regions characteristic of PTSD.The hippocampus plays a key role in memory, fear learning and extinction, and default mode network resting state connectivity, all processes which have known deficits in post‐traumatic stress disorder (PTSD). In this review, we examine recent fMRI studies on hippocampal function in PTSD and controls and identify critical areas for future research to explore.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/153031/1/psyp13357.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153031/2/psyp13357_am.pd

A practical scheme for quantum computation with any two-qubit entangling gate

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. Here we present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this important result for systems of arbitrary finite dimension has been provided by J. L. and R. Brylinski [arXiv:quant-ph/0108062, 2001]; however, their proof relies upon a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical [C. M. Dawson and A. Gilchrist, online implementation of the procedure described herein (2002), http://www.physics.uq.edu.au/gqc/].Comment: 3 pages, online implementation of procedure described can be found at http://www.physics.uq.edu.au/gqc

Intuiting a Monsoonal Ethnography in Three Bay of Bengal Cities

This visual essay offers an exploration of monsoonal materiality and agency in the urban environments of three cities situated around the Bay of Bengal: Chennai, Dhaka and Yangon. The text and images emerge from a research project exploring intersections between changing monsoon climates and rapid urbanisation in South Asia. Multi-modal, more-than-human ethnography has been employed during the course of research to explore how the lively materiality of the monsoon is entangled within urban lived environments. The essay outlines the process of intuiting a monsoonal ethnography and conveys the power of immersive field experience. By collecting and curating an assemblage of visual material and fieldnotes, this piece seeks to evoke the materiality and agency of the monsoon, itself a complex assemblage that manifests in different ways in different places. The juxtaposition of image and text conveys the generative and multifaceted agency of the monsoon and the urban environments it becomes enmeshed within

Lie group weight multiplicities from conformal field theory

Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of Wess-Zumino-Witten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among multiplicities. At least for some Lie groups, these new relations are strong enough to completely fix all multiplicities.Comment: 12 pages, Plain TeX, no figure

Plant communities affect arbuscular mycorrhizal fungal diversity and community composition in grassland microcosms

The diversity of arbuscular mycorrhizal (AM) fungi was investigated in an unfertilized limestone grassland soil supporting different synthesized vascular plant assemblages that had developed for 3 yr. The experimental treatments comprised: bare soil; monocultures of the nonmycotrophic sedge Carex flacca; monocultures of the mycotrophic grass Festuca ovina; and a species-rich mixture of four forbs, four grasses and four sedges. The diversity of AM fungi was analysed in roots of Plantago lanceolata bioassay seedlings using terminal-restriction fragment length polymorphism (T-RFLP). The extent of AM colonization, shoot biomass and nitrogen and phosphorus concentrations were also measured. The AM diversity was affected significantly by the floristic composition of the microcosms and shoot phosphorus concentration was positively correlated with AM diversity. The diversity of AM fungi in P. lanceolata decreased in the order: bare soil > C. flacca > 12 species > F. ovina. The unexpectedly high diversity in the bare soil and sedge monoculture likely reflects differences in the modes of colonization and sources of inoculum in these treatments compared with the assemblages containing established AM-compatible plants

Surface-acoustic-wave-driven luminescence from a lateral p-n junction

The authors report surface-acoustic-wave-driven luminescence from a lateral p-n junction formed by molecular beam epitaxy regrowth of a modulation doped GaAs/AlGaAs quantum well on a patterned GaAs substrate. Surface-acoustic-wave-driven transport is demonstrated by peaks in the electrical current and light emission from the GaAs quantum well at the resonant frequency of the transducer. This type of junction offers high carrier mobility and scalability. The demonstration of surface-acoustic-wave luminescence is a significant step towards single-photon applications in quantum computation and quantum cryptography.Comment: 4 pages, 3 figure

Bell Inequalities with Auxiliary Communication

What is the communication cost of simulating the correlations produced by quantum theory? We generalize Bell inequalities to the setting of local realistic theories augmented by a fixed amount of classical communication. Suppose two parties choose one of M two-outcome measurements and exchange 1 bit of information. We present the complete set of inequalities for M = 2, and the complete set of inequalities for the joint correlation observable for M = 3. We find that correlations produced by quantum theory satisfy both of these sets of inequalities. One bit of communication is therefore sufficient to simulate quantum correlations in both of these scenarios.Comment: 5 page

Unitary Gate Synthesis for Continuous Variable Systems

We investigate the synthesis of continuous-variable two-mode unitary gates in the setting where two modes A and B are coupled by a fixed quadratic Hamiltonian H. The gate synthesis consists of a sequence of evolutions governed by Hamiltonian H interspaced by local phase shifts applied to A and B. We concentrate on protocols that require the minimum necessary number of steps and we show how to implement the beam splitter and the two-mode squeezer in just three steps. Particular attention is paid to the Hamiltonian x_A p_B that describes the effective off-resonant interaction of light with the collective atomic spin.Comment: 7 pages, minor text modifications, references adde