Tri-hamiltonian vector fields, spectral curves and separation coordinates

We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson brackets (P_0, P_1, P_2), separation coordinates are provided by the common roots of a set of bivariate polynomials. These polynomials, which generalise those considered by E. Sklyanin in his algebro-geometric approach, are obtained from the knowledge of: (i) a common Casimir function for the two Poisson pencils (P_1 - \lambda P_0) and (P_2 - \mu P_0); (ii) a suitable set of vector fields, preserving P_0 but transversal to its symplectic leaves. The frameworks is applied to Lax equations with spectral parameter, for which not only it unifies the separation techniques of Sklyanin and of Magri, but also provides a more efficient ``inverse'' procedure not involving the extraction of roots.Comment: 49 pages Section on reduction revisite

Dark Energy Dominance and Cosmic Acceleration in First Order Formalism

The current accelerated universe could be produced by modified gravitational dynamics as it can be seen in particular in its Palatini formulation. We analyze here a specific non-linear gravity-scalar system in the first order Palatini formalism which leads to a FRW cosmology different from the purely metric one. It is shown that the emerging FRW cosmology may lead either to an effective quintessence phase (cosmic speed-up) or to an effective phantom phase. Moreover, the already known gravity assisted dark energy dominance occurs also in the first order formalism. Finally, it is shown that a dynamical theory able to resolve the cosmological constant problem exists also in this formalism, in close parallel with the standard metric formulation.Comment: 21 pages, LaTeX file, no figures. Replaced version to be published on Phys. Rev.

The dynamical equivalence of modified gravity revisited

We revisit the dynamical equivalence between different representations of vacuum modified gravity models in view of Legendre transformations. The equivalence is discussed for both bulk and boundary space, by including in our analysis the relevant Gibbons-Hawking terms. In the f(R) case, the Legendre transformed action coincides with the usual Einstein frame one. We then re-express the R+f(G) action, where G is the Gauss-Bonnet term, as a second order theory with a new set of field variables, four tensor fields and one scalar and study its dynamics. For completeness, we also calculate the conformal transformation of the full Jordan frame R+f(G) action. All the appropriate Gibbons-Hawking terms are calculated explicitly.Comment: 17 pages; v3: Revised version. New comments added in Sections 3 & 5. New results added in Section 6. Version to appear in Class. Quantum Gravit

Gauge Fixing in Higher Derivative Gravity

Linearized four-derivative gravity with a general gauge fixing term is considered. By a Legendre transform and a suitable diagonalization procedure it is cast into a second-order equivalent form where the nature of the physical degrees of freedom, the gauge ghosts, the Weyl ghosts, and the intriguing "third ghosts", characteristic to higher-derivative theories, is made explicit. The symmetries of the theory and the structure of the compensating Faddeev-Popov ghost sector exhibit non-trivial peculiarities.Comment: 21 pages, LaTe

Towards a multidimensional measure of well-being: cross-cultural support through the Italian validation of the well-being profile

Background The Well-being Profile (WB-Pro) is a multi-item and multidimensional instrument with strong psychometric properties and a solid theoretical grounding. It includes aspects of hedonic and eudaimonic well-being that can be used at the individual and social levels.MethodWe developed the Italian version through back-translation procedures. The aim of this study is to validate the WB-Pro in Italian as well as to better understand its multidimensionality through bifactor analysis. A sample of 1451 participants (910 = women, 62.7%; age range: 18-70, M-age = 32.34, SD-age = 13.64) was involved.ResultsThe 15-factor structure was confirmed with CFA and ESEM and was invariant across gender, age, and education. We examined convergent and discriminant validity and a bifactorial representation. Short versions of the WB-Pro were tested.DiscussionEven though a few items of the Italian version of the WB-Pro might benefit from revision (e.g., clear-thinking scale), this study confirms the theoretical and empirical strength of the WB-Pro.ConclusionsThis study supports the WB-Pro validity and usefulness in studying well-being and for professional psychological applications to assess well-being in both individuals and groups

Ostrogradski Formalism for Higher-Derivative Scalar Field Theories

We carry out the extension of the Ostrogradski method to relativistic field theories. Higher-derivative Lagrangians reduce to second differential-order with one explicit independent field for each degree of freedom. We consider a higher-derivative relativistic theory of a scalar field and validate a powerful order-reducing covariant procedure by a rigorous phase-space analysis. The physical and ghost fields appear explicitly. Our results strongly support the formal covariant methods used in higher-derivative gravity.Comment: 22 page

Functional anatomy of the masking level difference, an fMRI study

Introduction: Masking level differences (MLDs) are differences in the hearing threshold for the detection of a signal presented in a noise background, where either the phase of the signal or noise is reversed between ears. We use N0/Nπ to denote noise presented in-phase/out-of-phase between ears and S0/Sπ to denote a 500 Hz sine wave signal as in/out-of-phase. Signal detection level for the noise/signal combinations N0Sπ and NπS0 is typically 10-20 dB better than for N0S0. All combinations have the same spectrum, level, and duration of both the signal and the noise. Methods: Ten participants (5 female), age: 22-43, with N0Sπ-N0S0 MLDs greater than 10 dB, were imaged using a sparse BOLD fMRI sequence, with a 9 second gap (1 second quiet preceding stimuli). Band-pass (400-600 Hz) noise and an enveloped signal (.25 second tone burst, 50% duty-cycle) were used to create the stimuli. Brain maps of statistically significant regions were formed from a second-level analysis using SPM5. Results: The contrast NπS0- N0Sπ had significant regions of activation in the right pulvinar, corpus callosum, and insula bilaterally. The left inferior frontal gyrus had significant activation for contrasts N0Sπ-N0S0 and NπS0-N0S0. The contrast N0S0-N0Sπ revealed a region in the right insula, and the contrast N0S0-NπS0 had a region of significance in the left insula. Conclusion: Our results extend the view that the thalamus acts as a gating mechanism to enable dichotic listening, and suggest that MLD processing is accomplished through thalamic communication with the insula, which communicate across the corpus callosum to either enhance or diminish the binaural signal (depending on the MLD condition). The audibility improvement of the signal with both MLD conditions is likely reflected by activation in the left inferior frontal gyrus, a late stage in the what/where model of auditory processing. © 2012 Wack et al

The Universality of Einstein Equations

It is shown that for a wide class of analytic Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the so--called ``Palatini formalism'', i.e., treating the metric and the connection as independent variables, leads to ``universal'' equations. If the dimension $n$ of space--time is greater than two these universal equations are Einstein equations for a generic Lagrangian and are suitably replaced by other universal equations at bifurcation points. We show that bifurcations take place in particular for conformally invariant Lagrangians $L=R^{n/2} \sqrt g$ and prove that their solutions are conformally equivalent to solutions of Einstein equations. For 2--dimensional space--time we find instead that the universal equation is always the equation of constant scalar curvature; the connection in this case is a Weyl connection, containing the Levi--Civita connection of the metric and an additional vectorfield ensuing from conformal invariance. As an example, we investigate in detail some polynomial Lagrangians and discuss their bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9