Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a finite set of strata, which are semialgebraic manifolds formed by the $G$-orbits with the same orbit-type. In this paper we provide a simple recipe to obtain rational parametrizations of the strata. Our results can be easily exploited, in many physical contexts where the study of equivariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry breaking, in the analysis of phase spaces and structural phase transitions (Landau theory), in equivariant bifurcation theory, in crystal field theory and in most areas where use is made of symmetry adapted functions. A physically significant example of utilization of the recipe is given, related to spontaneous polarization in chiral biaxial liquid crystals, where the advantages with respect to previous heuristic approaches are shown.Comment: Figures generated through texdraw package; revised version appearing in J. Phys. A: Math. Ge

Geometric invariant theory approach to the determination of ground states of D-wave condensates in isotropic space

A complete and rigorous determination of the possible ground states for D-wave pairing Bose condensates is presented, using a geometrical invariant theory approach to the problem. The order parameter is argued to be a vector, transforming according to a ten dimensional real representation of the group $G=${\bf O}$_3\otimes${\bf U}$_1\times$. We determine the equalities and inequalities defining the orbit space of this linear group and its symmetry strata, which are in a one-to-one correspondence with the possible distinct phases of the system. We find 15 allowed phases (besides the unbroken one), with different symmetries, that we thoroughly determine. The group-subgroup relations between bordering phases are pointed out. The perturbative sixth degree corrections to the minimum of a fourth degree polynomial $G$-invariant free energy, calculated by Mermin, are also determined.Comment: 27 revtex pages, 2 figures, use of texdraw; minor changes in the bibliography and in Table II

Kinematics of the 1991 Randa rockslides (Valais, Switzerland)

International audienceAbout 22 mio m3 of rock fell from a cliff near the village of Randa (10 km north of Zermatt, Switzerland) on 18 April 1991. A second retrogressive rockslide of about 7 mio m3 followed on 9 May 1991. At present, a rock mass situated above the scarp is still slowly moving toward the valley, involving several mio m 3 of rock. A kinematic approach to study of this well-documented rockslide was made "a posteriori" in order to identify the parameters relevant to the detection of such failures involving large volumes of rock. A 3-D model of the pre-rockslide geometry is presented, and is used to interpret the geostructural, hydrogeological, and chronological data. The steepness of the cliff, the massive lithology (mainly orthogneiss), the location on a topographic ridge outcropping at the confluence between a glacial cirque and the main valley, and the existence of previous events of instability were the preexisting field conditions that affected the stability of the area. The structural cause of instability was a 30 dipping, more than 500-m-long, persistent fault, which cut the base of the rock face. Together with a steeply dipping set of persistent joints, this basal discontinuity delimited a 20- mio-m 3 rock block, with a potential sliding direction approximately parallel to the axis of the valley. To the North, the fractures delimiting the unstable mass were less persistent and separated by rock bridges; this rock volume acted as key block. This topographic and structural configuration was freed from glacier support about 15 000 years BP. The various mechanisms of degradation that led to the final loss of equilibrium required various amounts of time. During the late-and post-glacial periods, seismic activity and weathering of the orthogneiss along the fissure network due to infiltration of meteoric water, joined to reduce the mechanical resistance of the sliding surfaces and the rocks bridges. In addition, crystallisation of clay minerals due to mineralogical alteration of the fault gouge accumulated along the sliding surface, reducing its angle of internal friction, and sealing the surface against water circulation. Once this basal fracture began to act as an aquiclude, the seasonal increase of the hydraulic head in the fissures promoted hydraulic fracturing on the highly stressed edges of the key block. Acceleration of this mechanical degradation occurred during the 20-year period before the 1991 rockslides, giving rise to an increasing rockfall activity, that constituted a forewarning sign. The final triggering event corresponded to a snow-melt period with high water table, leading to fracturation around the key block. On 18 April 1991, the key block finally failed, allowing subsidiary orthogneiss blocks to slide. They fell in turn over a period of several hours. The 9 May 1991, rockslide was the first of a series of expected future retrogressive reequilibrium stages of the very fractured and decompressed paragneisses, which lie on the orthogneiss base cut by the 18 April event

The problem of political science and practical politics

Copyright @ 2006 The AuthorsWe reflect on the reasons why there is not a greater and more fruitful relationship between those who seek to understand policy and the political process from academia and those with a similar task in ‘practical politics’. We attribute this lack of engagement to three core factors: (1) from without, instrumental government visions of political science perpetuate the view that the discipline exists to serve those with power; (2) from within, scientism and abstraction diminish the discipline's stock of ‘usable’ product for ‘practical politics’; and (3) where relevant research exists, its uptake is hampered by limited communication between these spheres

Ultra-Low-Power Processors

Society's increasing use of connected sensing and wearable computing has created robust demand for ultra-low-power (ULP) edge computing devices and associated system-on-chip (SoC) architectures. In fact, the ubiquity of ULP processing has already made such embedded devices the highest-volume processor part in production, with an even greater dominance expected in the near future. The Internet of Everything calls for an embedded processor in every object, necessitating billions or trillions of processors. At the same time, the explosion of data generated from these devices, in conjunction with the traditional model of using cloud-based services to process the data, will place tremendous demands on limited wireless spectrum and energy-hungry wireless networks. Smart, ULP edge devices are the only viable option that can meet these demands

Global diversity of mayflies (Ephemeroptera, Insecta) in freshwater

The extant global Ephemeroptera fauna is represented by over 3,000 described species in 42 families and more than 400 genera. The highest generic diversity occurs in the Neotropics, with a correspondingly high species diversity, while the Palaearctic has the lowest generic diversity, but a high species diversity. Such distribution patterns may relate to how long evolutionary processes have been carrying on in isolation in a bioregion. Over an extended period, there may be extinction of species, but evolution of more genera. Dramatic extinction events such as the K-T mass extinction have affected current mayfly diversity and distribution. Climatic history plays an important role in the rate of speciation in an area, with regions which have been climatically stable over long periods having fewer species per genus, when compared to regions subjected to climatic stresses, such as glaciation. A total of 13 families are endemic to specific bioregions, with eight among them being monospecific. Most of these have restricted distributions which may be the result of them being the relict of a previously more diverse, but presently almost completely extinct family, or may be the consequence of vicariance events, resulting from evolution due to long-term isolation

Does This Patient Have Acute Mountain Sickness?: The Rational Clinical Examination Systematic Review.

Acute mountain sickness (AMS) affects more than 25% of individuals ascending to 3500 m (11 500 ft) and more than 50% of those above 6000 m (19 700 ft). AMS may progress from nonspecific symptoms to life-threatening high-altitude cerebral edema in less than 1% of patients. It is not clear how to best diagnose AMS. To systematically review studies assessing the accuracy of AMS diagnostic instruments, including the visual analog scale (VAS) score, which quantifies the overall feeling of sickness at altitude (VAS[O]; various thresholds), Acute Mountain Sickness-Cerebral score (AMS-C; ≥0.7 indicates AMS), and the clinical functional score (CFS; ≥2 indicates AMS) compared with the Lake Louise Questionnaire Score (LLQS; score of ≥5). Searches of MEDLINE and EMBASE from inception to May 2017 identified 1245 publications of which 91 were suitable for prevalence analysis (66 944 participants) and 14 compared at least 2 instruments (1858 participants) using a score of 5 or greater on the LLQS as a reference standard. To determine the prevalence of AMS for establishing the pretest probability of AMS, a random-effects meta-regression was performed based on the reported prevalence of AMS as a function of altitude. AMS prevalence, likelihood ratios (LRs), sensitivity, and specificity of screening instruments. The final analysis included 91 articles (comprising 66 944 study participants). Altitude predicted AMS and accounted for 28% of heterogeneity between studies. For each 1000-m (3300-ft) increase in altitude above 2500 m (8200 ft), AMS prevalence increased 13% (95% CI, 9.5%-17%). Testing characteristics were similar for VAS(O), AMS-C, and CFS vs a score of 5 or greater on the LLQS (positive LRs: range, 3.2-8.2; P = .22 for comparisons; specificity range, 67%-92%; negative LRs: range, 0.30-0.36; P = .50 for comparisons; sensitivity range, 67%-82%). The CFS asks a single question: "overall if you had any symptoms, how did they affect your activity (ordinal scale 0-3)?" For CFS, moderate to severe reduction in daily activities had a positive LR of 3.2 (95% CI, 1.4-7.2) and specificity of 67% (95% CI, 37%-97%); no reduction to mild reduction in activities had a negative LR of 0.30 (95% CI, 0.22-0.39) and sensitivity of 82% (95% CI, 77%-87%). The prevalence of acute mountain sickness increases with higher altitudes. The visual analog scale for the overall feeling of sickness at altitude, Acute Mountain Sickness-Cerebral, and clinical functional score perform similarly to the Lake Louise Questionnaire Score using a score of 5 or greater as a reference standard. In clinical and travel settings, the clinical functional score is the simplest instrument to use. Clinicians evaluating high-altitude travelers who report moderate to severe limitations in activities of daily living (clinical functional score ≥2) should use the Lake Louise Questionnaire Score to assess the severity of acute mountain sickness

Análise do comportamento de matrizes suínas lactantes com o uso de enriquecimento ambiental na maternidade.

Projeto/Plano de Ação: 02.09.07.007

'Word from the street' : when non-electoral representative claims meet electoral representation in the United Kingdom

Taking the specific case of street protests in the UK – the ‘word from the street’– this article examines recent (re)conceptualizations of political representation, most particularly Saward’s notion of ‘representative claim’. The specific example of nonelectoral claims articulated by protestors and demonstrators in the UK is used to illustrate: the processes of making, constituting, evaluating and accepting claims for and by constituencies and audiences; and the continuing distinctiveness of claims based upon electoral representation. Two basic questions structure the analysis: first, why would the political representative claims of elected representatives trump the nonelectoral claims of mass demonstrators and, second, in what ways does the ‘perceived legitimacy’ of the former differ from the latter