Geodesics on Lie groups: Euler equations and totally geodesic subgroup

The geodesic motion on a Lie group equipped with a left or right invariant Riemannian metric is governed by the Euler-Arnold equation. This paper investigates conditions on the metric in order for a given subgroup to be totally geodesic. Results on the construction and characterisation of such metrics are given. The setting works both in the classical nite dimensional case, and in the category of in nite dimensional Fr echet Lie groups, in which di eomorphism groups are included. Using the framework we give new examples of both nite and in nite dimensional totally geodesic subgroups. In particular, based on the cross helicity, we construct right invariant metrics such that a given subgroup of exact volume preserving di eomorphisms is totally geodesic. The paper also gives a general framework for the representation of Euler-Arnold equations in arbitrary choice of dual pairing

Higher Order Effects in the Dielectric Constant of Percolative Metal-Insulator Systems above the Critical Point

The dielectric constant of a conductor-insulator mixture shows a pronounced maximum above the critical volume concentration. Further experimental evidence is presented as well as a theoretical consideration based on a phenomenological equation. Explicit expressions are given for the position of the maximum in terms of scaling parameters and the (complex) conductances of the conductor and insulator. In order to fit some of the data, a volume fraction dependent expression for the conductivity of the more highly conductive component is introduced.Comment: 4 pages, Latex, 4 postscript (*.epsi) files submitted to Phys Rev.

A learning community two years on: reflecting on successes and framing futures

This paper reports the results of a participatory action research (PAR) evaluation conducted with the members of the Granite Belt Learners Group in their rural 'learning community' in South East Queensland, and presents an action research and evaluation framework to guide the community on the next stage of its journey

Finite-size effects on the Hamiltonian dynamics of the XY-model

The dynamical properties of the finite-size magnetization M in the critical region T<T_{KTB} of the planar rotor model on a L x L square lattice are analyzed by means of microcanonical simulations . The behavior of the q=0 structure factor at high frequencies is consistent with field-theoretical results, but new additional features occur at lower frequencies. The motion of M determines a region of spectral lines and the presence of a central peak, which we attribute to phase diffusion. Near T_{KTB} the diffusion constant scales with system size as D ~ L^{-1.6(3)}.Comment: To be published in Europhysics Letter

A mixed-methods study of the implementation of medication adherence policy solutions: how do European countries compare?

Wendy Clyne,1 Sarah McLachlan2 1Faculty of Health and Life Sciences, Coventry University, Priory Street, Coventry, UK; 2Primary Care and Health Sciences, Keele University, Staffordshire, UK Objectives: We describe a key informant study that invited national medicines policy leads for the European Union member states to self-assess the level of implementation of medicines adherence initiatives in their country and the adequacy of that implementation. Interviews with medicines policy leads enabled in-depth understanding of the variation in adherence support across nations and the ways in which different nations prioritize, plan, and implement medicines adherence systems and services.Methods: Ten national policy leads (Bulgaria, Denmark, Estonia, Finland, Germany, Ireland, Latvia, Lithuania, Malta, and the Netherlands) completed a self-assessment survey, and seven (Estonia, Finland, Germany, Ireland, Lithuania, Malta, and the Netherlands) engaged in a follow-up interview.Key findings: Policy leads varied in the level of implementation of medication adherence solutions that they reported in their nations; most initiatives were aimed directly at patients with few initiatives at government or health care commissioner levels of action. Policy leads reported insufficient implementation of medication adherence initiatives across all potential domains. Barriers to implementation included lack of resources, strategic planning, evidence to support action, the &ldquo;hidden&rdquo; nature of medication adherence within policy work, and dispersed responsibility for medication adherence as a policy and practice theme.Conclusion: This study has international significance and summarizes the emergent characteristics of nations with and without coordinated medication adherence activity. We highlight the importance of sharing good practice in policy formulation and implementation for medication adherence. Keywords: medication adherence, policy implementation, medicines policy, health care polic

The configuration and relations of the pituitary gland and fossa: a radiological, pathological and clinical study

In 50 adult necropsies, measurements of linear dimensions and volume of the normal pituitary gland were correlated with corresponding measurements of the sella turcica obtained from radiographs. Though the female pituitary gland was significantly larger than the male, there was no significant sex difference in sellar size. Dimensions of gland and fossa were correlated separately for each sex. Correlation between gland volume and estimated sellar volume was good. The length of the sella and the width of its floor correlated well with the length and-width of the gland, but correlation between measurements of sellar height and gland height was poor, especially in women.Detailed studies of the radiological anatomy of these glands and fossae showed wide variation in the configuration of the diaphragma sellae, particularly in the position of its central portion relative to bony landmarks. In several a sub-diaphragmatic extension of the subarachnoid space was found. The shape of the gland varied markedly and was frequently distorted by compression by the carotid arteries. Bony configuration was also altered by these arteries which in some cases eroded the lateral margins of the dorsum sellae, undercutting the posterior clinoid processes. Some other variations in sellar contour are illustrated and discussed.To evaluate radiological criteria of abnormality in the light of such wide normal variation, radiographs of the pituitary fossa of 140 acromegalic patients were assessed. Over half were grossly abnormal, showing marked bony erosion and enlargement. In a quarter, a double sellar contour was present, but, since dimensions of the inner contour were normal or only slightly enlarged, abnormality was often overlooked. The remainder (18%) presented particular diagnostic difficulty. On plain films, commonly accepted criteria of abnormality discriminated poorly between this group and controls. Measurement of sellar dimensions, because of the wide normal range, was also unhelpful. However, tomography of the sella demonstrated significant abnormality in almost all and frequently revealed downward extension of the pituitary tumour unsuspected on plain films. Combined assessment by plain films and tomography showed sellar abnormality in nearly 99% of the 140 patients.To demonstrate suprasellar anatomy, tomography in two planes was combined with pneumoencephalography in 37 patients suffering from various types of pituitary tumour. Examinations were successful in all but one, showing a wide variation in the position of the superior aspect of the tumour. Suprasellar extensions were not predictable on the basis of bony configuration of the sella and frequently failed to produce visual field defects. Subarachnoid extensions into the sella were also demonstrated. Attention is drawn to the implications of these variations and the importance of their demonstration before therapeutic procedures on the pituitary gland are undertaken

Dimension-adaptive bounds on compressive FLD Classification

Efficient dimensionality reduction by random projections (RP) gains popularity, hence the learning guarantees achievable in RP spaces are of great interest. In finite dimensional setting, it has been shown for the compressive Fisher Linear Discriminant (FLD) classifier that forgood generalisation the required target dimension grows only as the log of the number of classes and is not adversely affected by the number of projected data points. However these bounds depend on the dimensionality d of the original data space. In this paper we give further guarantees that remove d from the bounds under certain conditions of regularity on the data density structure. In particular, if the data density does not fill the ambient space then the error of compressive FLD is independent of the ambient dimension and depends only on a notion of ‘intrinsic dimension'

Matter-screened Casimir force and Casimir-Polder force in planar structures

Using a recently developed theory of the Casimir force (Raabe C and Welsch D-G 2005 Phys. Rev. A 71 013814), we calculate the force that acts on a plate in front of a planar wall and the force that acts on the plate in the case where the plate is part of matter that fills the space in front of the wall. We show that in the limit of a dielectric plate whose permittivity is close to unity, the force obtained in the former case reduces to the ordinary, i.e., unscreened Casimir-Polder force acting on isolated atoms. In the latter case, the theory yields the Casimir-Polder force that is screened by the surrounding matter.Comment: 11 pages, 1 figure -- published online at J. Opt. B on Nov 16 200