Lie symmetries of Einstein's vacuum equations in N dimensions

We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on Einstein's equations. Instead of setting to zero the coefficients of all independent partial derivatives (which involves a very complicated substitution of Einstein's equations), we set to zero the coefficients of derivatives that do not appear in Einstein's equations. This considerably constrains the coefficients of symmetry generating vector fields. Using the Lie algebra property of generators of symmetries and the fact that general coordinate transformations are symmetries of Einstein's equations, we are then able to obtain all the Lie symmetries. The method we have used can likely be applied to other types of equations

Giant Alcohol: A Worthy Opponent for the Children of the Band of Hope

From its foundation in 1847, the temperance organisation the Band of Hope addressed its young members as consumers, victims, and agents. In the first two roles they encountered the effects of drink of necessity, but in the third role they were encouraged to seek it out, attempting to influence individuals and wider society against 'Giant Alcohol'. With an estimated membership of half the school-age population by the early twentieth century, well over three million, the Band of Hope also acted more directly to influence policy, and encouraged young people to consider issues of policy and politics. With its wide range of activities and material to educate, entertain and empower millions of children, and its radical view of the place of the child, the Band of Hope not only mobilised its child members to lobby for legal change, including prohibition, but took an active part in pointing out the cost of alcohol to society, particularly during the 14-18 war. The organisation began to decline post 1918, and this paper focuses on the address made to children by the Band of Hope in the late nineteenth and early twentieth centuries, at a time when its innovative view of children as able to understand and influence policy decisions reflected developments in the construction of childhood. This article draws on the archive of the British National Temperance League, over 50,000 items located in the Livesey Collection, University of Central Lancashire

Discriminating among Earth composition models using geo-antineutrinos

It has been estimated that the entire Earth generates heat corresponding to about 40 TW (equivalent to 10,000 nuclear power plants) which is considered to originate mainly from the radioactive decay of elements like U, Th and K, deposited in the crust and mantle of the Earth. Radioactivity of these elements produce not only heat but also antineutrinos (called geo-antineutrinos) which can be observed by terrestrial detectors. We investigate the possibility of discriminating among Earth composition models predicting different total radiogenic heat generation, by observing such geo-antineutrinos at Kamioka and Gran Sasso, assuming KamLAND and Borexino (type) detectors, respectively, at these places. By simulating the future geo-antineutrino data as well as reactor antineutrino background contributions, we try to establish to which extent we can discriminate among Earth composition models for given exposures (in units of kt$\cdot$ yr) at these two sites on our planet. We use also information on neutrino mixing parameters coming from solar neutrino data as well as KamLAND reactor antineutrino data, in order to estimate the number of geo-antineutrino induced events.Comment: 24 pages, 10 figures, final version to appear in JHE

Newly identified properties of surface acoustic power

The cause of enhanced acoustic power surrounding active regions, the acoustic halo, is not as yet understood. We explore the properties of the enhanced acoustic power observed near disk center from 21 to 27 January 2002, including AR 9787. We find that (i) there exists a strong correlation of the enhanced high frequency power with magnetic-field inclination, with greater power in more horizontal fields, (ii) the frequency of the maximum enhancement increases along with magnetic field strength, and (iii) the oscillations contributing to the halos show modal ridges which are shifted to higher wavenumber at constant frequency in comparison to the ridges of modes in the quiet-Sun.Comment: 16 pages, 10 figures, submitted to solar physic

The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - II: Dirac versus Bergmann observables and the Objectivity of Space-Time

(abridged)The achievements of the present work include: a) A clarification of the multiple definition given by Bergmann of the concept of {\it (Bergmann) observable. This clarification leads to the proposal of a {\it main conjecture} asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). b) The analysis of the so-called {\it Hole} phenomenology in strict connection with the Hamiltonian treatment of the initial value problem in metric gravity for the class of Christoudoulou -Klainermann space-times, in which the temporal evolution is ruled by the {\it weak} ADM energy. It is crucial the re-interpretation of {\it active} diffeomorphisms as {\it passive and metric-dependent} dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (nearly unknown) connection to gauge transformations on-shell; this is expounded in the first paper (gr-qc/0403081). The use of the Bergmann-Komar {\it intrinsic pseudo-coordinates} allows to construct a {\it physical atlas} of 4-coordinate systems for the 4-dimensional {\it mathematical} manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent {\it Dirac observables}), and to realize the {\it physical individuation} of the points of space-time as {\it point-events} as a gauge-fixing problem, also associating a non-commutative structure to each 4-coordinate system.Comment: 41 pages, Revtex

Depression rating scales in Parkinson's disease: critique and recommendations.

Depression is a common comorbid condition in Parkinson’s disease (PD) and a major contributor to poor quality of life and disability. However, depression can be difficult to assess in patients with PD due to overlapping symptoms and difficulties in the assessment of depression in cognitively impaired patients. As several rating scales have been used to assess depression in PD (dPD), the Movement Disorder Society commissioned a task force to assess their clinimetric properties and make clinical recommendations regarding their use. A systematic literature review was conducted to explore the use of depression scales in PD and determine which scales should be selected for this review. The scales reviewed were the Beck Depression Inventory (BDI), Hamilton Depression Scale (Ham-D), Hospital Anxiety and Depression Scale (HADS), Zung Self-Rating Depression Scale (SDS), Geriatric Depression Scale (GDS), Montgomery-As-berg Depression Rating Scale (MADRS), Unified Parkinson’s Disease Rating Scale (UPDRS) Part I, Cornell Scale for the Assessment of Depression in Dementia (CSDD), and the Center for Epidemiologic Studies Depression Scale (CES-D). Seven clinical researchers with clinical and research experience in the assessment of dPD were assigned to review the scales using a structured format. The most appropriate scale is dependent on the clinical or research goal. However, observer-rated scales are preferred if the study or clinical situation permits. For screening purposes, the HAM-D, BDI, HADS, MADRS, and GDS are valid in dPD. The CES-D and CSDD are alternative instruments that need validation in dPD. For measurement of severity of depressive symptoms, the Ham-D, MADRS, BDI, and SDS scales are recommended. Further studies are needed to validate the CSDD, which could be particularly useful for the assessment of severity of dPD in patients with comorbid dementia. To account for overlapping motor and nonmotor symptoms of depression, adjusted instrument cutoff scores may be needed for dPD, and scales to assess severity of motor symptoms (e.g., UPDRS) should also be included to help adjust for confounding factors. The HADS and the GDS include limited motor symptom assessment and may, therefore, be most useful in rating depression severity across a range of PD severity; however, these scales appear insensitive in severe depression. The complex and time-consuming task of developing a new scale to measure depression specifically for patients with PD is currently not warranted

Euclidean Approach to the Entropy for a Scalar Field in Rindler-like Space-Times

The off-shell entropy for a massless scalar field in a D-dimensional Rindler-like space-time is investigated within the conical Euclidean approach in the manifold C_\be\times\M^N, C_\be being the 2-dimensional cone, making use of the zeta-function regularisation. Due to the presence of conical singularities, it is shown that the relation between the zeta-function and the heat kernel is non trivial and, as first pointed out by Cheeger, requires a separation between small and large eigenvalues of the Laplace operator. As a consequence, in the massless case, the (naive) non existence of the Mellin transform is by-passed by the Cheeger's analytical continuation of the zeta-function on manifold with conical singularities. Furthermore, the continuous spectrum leads to the introduction of smeared traces. In general, it is pointed out that the presence of the divergences may depend on the smearing function and they arise in removing the smearing cutoff. With a simple choice of the smearing function, horizon divergences in the thermodynamical quantities are recovered and these are similar to the divergences found by means of off-shell methods like the brick wall model, the optical conformal transformation techniques or the canonical path integral method.Comment: 17 pages, LaTex. A sign error corrected and few comments adde

Latitudinal variation in ecological opportunity and intraspecific competition indicates differences in niche variability and diet specialization of Arctic marine predators

Individual specialization (IS), where individuals within populations irrespective of age, sex, and body size are either specialized or generalized in terms of resource use, has implications on ecological niches and food web structure. Niche size and degree of IS of near‐top trophic‐level marine predators have been little studied in polar regions or with latitude. We quantified the large‐scale latitudinal variation of population‐ and individual‐level niche size and IS in ringed seals (Pusa hispida) and beluga whales (Delphinapterus leucas) using stable carbon and nitrogen isotope analysis on 379 paired ringed seal liver and muscle samples and 124 paired beluga skin and muscle samples from eight locations ranging from the low to high Arctic. We characterized both within‐ and between‐individual variation in predator niche size at each location as well as accounting for spatial differences in the isotopic ranges of potential prey. Total isotopic niche width (TINW) for populations of ringed seals and beluga decreased with increasing latitude. Higher TINW values were associated with greater ecological opportunity (i.e., prey diversity) in the prey fish community which mainly consists of Capelin (Mallotus villosus) and Sand lance (Ammodytes sp.) at lower latitudes and Arctic cod (Boreogadus saida) at high latitudes. In beluga, their dietary consistency between tissues also known as the within‐individual component (WIC) increased in a near 1:1 ratio with TINW (slope = 0.84), suggesting dietary generalization, whereas the slope (0.18) of WIC relative to TINW in ringed seals indicated a high degree of individual specialization in ringed seal populations with higher TINWs. Our findings highlight the differences in TINW and level of IS for ringed seals and beluga relative to latitude as a likely response to large‐scale spatial variation in ecological opportunity, suggesting species‐specific variation in dietary plasticity to spatial differences in prey resources and environmental conditions in a rapidly changing ecosystem

Latitudinal variation in ecological opportunity and intraspecific competition indicates differences in niche variability and diet specialization of Arctic marine predators

Individual specialization (IS), where individuals within populations irrespective of age, sex, and body size are either specialized or generalized in terms of resource use, has implications on ecological niches and food web structure. Niche size and degree of IS of near‐top trophic‐level marine predators have been little studied in polar regions or with latitude. We quantified the large‐scale latitudinal variation of population‐ and individual‐level niche size and IS in ringed seals (Pusa hispida) and beluga whales (Delphinapterus leucas) using stable carbon and nitrogen isotope analysis on 379 paired ringed seal liver and muscle samples and 124 paired beluga skin and muscle samples from eight locations ranging from the low to high Arctic. We characterized both within‐ and between‐individual variation in predator niche size at each location as well as accounting for spatial differences in the isotopic ranges of potential prey. Total isotopic niche width (TINW) for populations of ringed seals and beluga decreased with increasing latitude. Higher TINW values were associated with greater ecological opportunity (i.e., prey diversity) in the prey fish community which mainly consists of Capelin (Mallotus villosus) and Sand lance (Ammodytes sp.) at lower latitudes and Arctic cod (Boreogadus saida) at high latitudes. In beluga, their dietary consistency between tissues also known as the within‐individual component (WIC) increased in a near 1:1 ratio with TINW (slope = 0.84), suggesting dietary generalization, whereas the slope (0.18) of WIC relative to TINW in ringed seals indicated a high degree of individual specialization in ringed seal populations with higher TINWs. Our findings highlight the differences in TINW and level of IS for ringed seals and beluga relative to latitude as a likely response to large‐scale spatial variation in ecological opportunity, suggesting species‐specific variation in dietary plasticity to spatial differences in prey resources and environmental conditions in a rapidly changing ecosystem