Algebraic methods in the theory of generalized Harish-Chandra modules

This paper is a review of results on generalized Harish-Chandra modules in the framework of cohomological induction. The main results, obtained during the last 10 years, concern the structure of the fundamental series of $(\mathfrak{g},\mathfrak{k})-$modules, where $\mathfrak{g}$ is a semisimple Lie algebra and $\mathfrak{k}$ is an arbitrary algebraic reductive in $\mathfrak{g}$ subalgebra. These results lead to a classification of simple $(\mathfrak{g},\mathfrak{k})-$modules of finite type with generic minimal $\mathfrak{k}-$types, which we state. We establish a new result about the Fernando-Kac subalgebra of a fundamental series module. In addition, we pay special attention to the case when $\mathfrak{k}$ is an eligible $r-$subalgebra (see the definition in section 4) in which we prove stronger versions of our main results. If $\mathfrak{k}$ is eligible, the fundamental series of $(\mathfrak{g},\mathfrak{k})-$modules yields a natural algebraic generalization of Harish-Chandra's discrete series modules.Comment: Keywords : generalized Harish-Chandra module, (g,k)-module of finite type, minimal k-type, Fernando-Kac subalgebra, eligible subalgebra; Pages no. : 13; Bibliography : 21 item

Multiplicity one theorems: the Archimedean case

Let $G$ be one of the classical Lie groups \GL_{n+1}(\R), \GL_{n+1}(\C), \oU(p,q+1), \oO(p,q+1), \oO_{n+1}(\C), \SO(p,q+1), \SO_{n+1}(\C), and let $G'$ be respectively the subgroup \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \oO(p,q), \oO_n(\C), \SO(p,q), \SO_n(\C), embedded in $G$ in the standard way. We show that every irreducible Casselman-Wallach representation of $G'$ occurs with multiplicity at most one in every irreducible Casselman-Wallach representation of $G$. Similar results are proved for the Jacobi groups \GL_{n}(\R)\ltimes \oH_{2n+1}(\R), \GL_{n}(\C)\ltimes \oH_{2n+1}(\C), \oU(p,q)\ltimes \oH_{2p+2q+1}(\R), \Sp_{2n}(\R)\ltimes \oH_{2n+1}(\R), \Sp_{2n}(\C)\ltimes \oH_{2n+1}(\C), with their respective subgroups \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \Sp_{2n}(\R), \Sp_{2n}(\C).Comment: To appear in Annals of Mathematic

Myrtle rust surveys of Eastern Australia

Records of Rhodomyrtus psidioides and their level of myrtle rust damage from Eastern Australia from field survey and personal communication with experts

Pain stages of change: Variations in pain acceptance, catastrophizing, and emotional distress across a model of readiness for behavior change

Pain often signals a problem that needs our attention, but after healing has occurred and pain persists, protective behaviors may become maladaptive to day-to-day functioning. Through education, therapy, and self-management, individuals can learn to function well on a daily basis even with some pain present, but not all pain patients are ready for this type of self-management. The transtheoretical model has been adapted to assess individuals with chronic pain. If individuals are not ready for behavior change, relapse chances increase; therefore it becomes beneficial to understand an individual\u27s level of readiness to change when judging potential treatment success. The ability of current pain stages of change instruments to categorize individuals into distinct groups has been limited. The first purpose of the current study was to analyze the relationship between chronic pain acceptance and cognitive and emotional distress related to pain. Results showed chronic pain acceptance did significantly correlate with both catastrophizing and emotional distress in a negative direction. The second purpose was to explore the relationship between acceptance, cognitive distress, and emotional distress related to pain, and stages of behavior change. Groups formed by the Freiburg Questionnaire-Stages of Chronic Pain Management (FQ-STAPM) were expected to vary significantly on acceptance of pain. Results indicated that individuals in the maintenance stage had significantly higher acceptance scores compared to individuals in each of the other three stages, and individuals in the action stage scored significantly higher than those in the preparation stage. It was also hypothesized that FQ-STAPM groups would vary significantly on measures of cognitive and emotional distress. The maintenance group did in fact have significantly lower levels of cognitive and emotional distress compared to the precontemplation and preparation groups. The action group also scored significantly lower on these measures compared to individuals in the preparation group. Participants from this study seemed to endorse different emotional and cognitive qualities across the stages of behavior change readiness. Those who endorsed items within the precontemplation and preparation subscales report moderate to high levels of emotional and cognitive distress according to their responses on the PDI and PCS. They also reported a moderate level of unwillingness to experience pain. These results offer significant theoretical and clinical implications. Individuals with chronic pain experience distinctly different types of emotional and cognitive distress as they deal with pain. Clinicians may also need to realize that even though lowering distress is important, a certain amount of distress may propel patients to take action toward self-management of pain symptoms. Acceptance of chronic pain also appears to be an important variable in successful self-maintenance of pain symptoms

Four-qubit entanglement from string theory

We invoke the black hole/qubit correspondence to derive the classification of four-qubit entanglement. The U-duality orbits resulting from timelike reduction of string theory from D=4 to D=3 yield 31 entanglement families, which reduce to nine up to permutation of the four qubits.Comment: 4 pages, 1 figure, 2 tables, revtex; minor corrections, references adde

Analysing the impact of iron dysmetabolism on regional metal ion distribution in the brain

An Iron Overload and an H-Ferritin Deficient Mouse Model were used to examine the impact of disrupted iron metabolism on the brain. Brain sections were imaged and compared using Synchrotron μXRF spectroscopy. Quantitative measurement of the relative metal ion concentrations for iron, copper and zinc were made across selected regions of interest in the brain. It was generally found that metal ion concentrations of iron and zinc decreased in specific regions in the Iron Overload condition compared with the control, with copper increasing in only one region. Few regions differed in metal ion concentration between the H-Ferritin Deficient Model and the control. The three conditions exhibited similar / identical results for metal ion concentrations in many brain regions, indicating the validity of the method used for comparison between samples. It is clear that there exists a complex relationship between these trace metal

Rigid surface operators and S-duality: some proposals

We study surface operators in the N=4 supersymmetric Yang-Mills theories with gauge groups SO(n) and Sp(2n). As recently shown by Gukov and Witten these theories have a class of rigid surface operators which are expected to be related by S-duality. The rigid surface operators are of two types, unipotent and semisimple. We make explicit proposals for how the S-duality map should act on unipotent surface operators. We also discuss semisimple surface operators and make some proposals for certain subclasses of such operators.Comment: 27 pages. v2: minor changes, added referenc

Iron stored in ferritin is chemically reduced in the presence of aggregating Aβ(1-42).

Atypical low-oxidation-state iron phases in Alzheimer's disease (AD) pathology are implicated in disease pathogenesis, as they may promote elevated redox activity and convey toxicity. However, the origin of low-oxidation-state iron and the pathways responsible for its formation and evolution remain unresolved. Here we investigate the interaction of the AD peptide β-amyloid (Aβ) with the iron storage protein ferritin, to establish whether interactions between these two species are a potential source of low-oxidation-state iron in AD. Using X-ray spectromicroscopy and electron microscopy we found that the co-aggregation of Aβ and ferritin resulted in the conversion of ferritin's inert ferric core into more reactive low-oxidation-states. Such findings strongly implicate Aβ in the altered iron handling and increased oxidative stress observed in AD pathogenesis. These amyloid-associated iron phases have biomarker potential to assist with disease diagnosis and staging, and may act as targets for therapies designed to lower oxidative stress in AD tissue

Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices

This paper is mainly a review of the multi--Hamiltonian nature of Toda and generalized Toda lattices corresponding to the classical simple Lie groups but it includes also some new results. The areas investigated include master symmetries, recursion operators, higher Poisson brackets, invariants and group symmetries for the systems. In addition to the positive hierarchy we also consider the negative hierarchy which is crucial in establishing the bi--Hamiltonian structure for each particular simple Lie group. Finally, we include some results on point and Noether symmetries and an interesting connection with the exponents of simple Lie groups. The case of exceptional simple Lie groups is still an open problem.Comment: 65 pages, 67 reference

People with aphasia creating an aphasia friendly website: The DMU4 experience

People with aphasia creating an aphasia friendly website: The DMU4 experience Bixley,M., DMU4, Hall, R., Weale, R., Collingwood, J., Marshall, F. & Hamilton, C. Background Information The DMU4 Conversation group is part of Aphasia Leicester; a community based, voluntary sector, long term support organisation for People with Aphasia (PWA). Members of DMU4 have experienced being unable to access information about their condition because of the way in which the information is presented. These personal experiences are supported by research such as the Care Quality Commission’s (2011) report that suggested that only 40% of social services in Britain provided information in an accessible way for PWA post stroke. In 2011, DMU4 created a leaflet about aphasia that was designed to be used in acute hospitals to educate stroke survivors, relatives and hospital staff about aphasia (Bixley et al, 2011). This leaflet has been distributed to hospitals, surgeries and Speech and Language Therapy Departments in Leicestershire and Rutland. Last year DMU4 decided that they would like to embark on a new project; creating a website about aphasia that was also accessible to PWA. Method The group decided that there were three main factors that needed to guide the construction and structure of the website. Firstly, people with aphasia would appear on the website as aphasia experts. Secondly, navigation around the website should be aphasia friendly, based on visual images and accessible written language. Lastly, members of DMU4 would retain copyright over their own images. For this reason, the site was hosted on “Our DMU Commons” a self organising space that allows users to co construct their own website using open source software. The content of the website was agreed through group discussions. Following these discussions, nine DMU4 members attended a whole day filming session in which their perceptions of aphasia were recorded. Films were then transcribed and edited into eleven themes using a grounded approach. Skeat & Perry (2007) suggest this approach is useful when investigating information that is not available anywhere else, such as the information presented in this website. Informed consent was elicited through discussions, meetings, film and website screenings and signed agreement. Results and discussion The DMU4 website project has two tangible outcomes. The first is that the site will be available to people who want to learn about aphasia. The second is that the resource will be available for Speech and Language Therapy students. Learning activities will enable students to practise recognising and understand aphasia from the perspective of those who live with the loss of language post stroke. The practices of DMU4 are rooted firmly in the social approach to aphasia therapy (Pound, Parr, Lindsay and Woolf, 2000). It is hoped that the website’s third, less measurable, outcome will be a contribution to overcoming the attitudinal and informational barriers that are experienced by PWA post stoke. References BIXLEY, M., DMU4 & HAMILTON, C. (2011) Aphasia – an information leaflet designed by people with aphasia. British Aphasiology Society Biennial International Conference Book of Abstracts, 12. CARE QUALITY COMMISSION (2011) Supporting life after stroke: A review of services for people who have had a stroke and their carers. London: Care Quality Commission. SKEAT, J. & PERRY, A. (2008). Grounded theory as a method for research in speech and language therapy. International Journal of Language and Communication Disorders, 43, 2, 95-109. POUND, C., PARR, S., LINDSAY, J. & WOOLF, C. (2000) Beyond Aphasia: Therapies for Living with Communication Disability. Bicester: Winslow