Universality of Einstein Equations for the Ricci Squared Lagrangians

It has been recently shown that, in the first order (Palatini) formalism, there is universality of Einstein equations and Komar energy-momentum complex, in the sense that for a generic nonlinear Lagrangian depending only on the scalar curvature of a metric and a torsionless connection one always gets Einstein equations and Komar's expression for the energy-momentum complex. In this paper a similar analysis (also in the framework of the first order formalism) is performed for all nonlinear Lagrangians depending on the (symmetrized) Ricci square invariant. The main result is that the universality of Einstein equations and Komar energy-momentum complex also extends to this case (modulo a conformal transformation of the metric).Comment: 21 pages, Late

Universities multistakeholder contribution to smart city ecosystem development

Purpose: This paper investigates the mutually advantageous value-driven innovations brought by Universities as a key actor in the development of innovation exploiting Smart City opportunities. The final aim is to under-stand the role, tasks and contribution of Universities in Smart City pro-jects. Methodology: The study followed an exploratory and qualitative meth-odology and consisted of 44 in-depth semi-structured interviews with Smart City experts. The choice of the respondents was adjusted to approve the direct and indirect effect of developing the smart ecosystem in various organizational multistakeholder environments. Results: The study found three main areas in which Universities may con-tribute to Smart City projects: a) knowledge/technology creation and transfer; b) social/societal involvement; c) ecosystem facilita-tor/networking.Implications: This paper offers several implications for different stake-holders such as policy makers, Universities’ top managers and firms. Impli-cations for policy managers imply the change in the approach to consumers because most of them do not understand why they need smart solutions. Moreover, it highlights that bureaucracy and lack of an innovative mental-ity kill smart city projects, so the governmental structures should be wired first. Finally, it calls for a huge financial platform (incentives and new fi-nancial mechanisms) and legal changes (legal frameworks should be aligned with peculiarities of Smart Cities).Implications for top managers of Universities are related to the rethink of Universities in smart city innovation ecosystems with the possibility to play an active role. Implications for MNEs and SMEs include that Univer-sities may help in understanding the opportunities around Smart City initi-atives (there is often opacity on the return of investments). At the same time, Universities may help in dealing with public governments and local stakeholders (public and private)

Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries

A general recipe to define, via Noether theorem, the Hamiltonian in any natural field theory is suggested. It is based on a Regge-Teitelboim-like approach applied to the variation of Noether conserved quantities. The Hamiltonian for General Relativity in presence of non-orthogonal boundaries is analysed and the energy is defined as the on-shell value of the Hamiltonian. The role played by boundary conditions in the formalism is outlined and the quasilocal internal energy is defined by imposing metric Dirichlet boundary conditions. A (conditioned) agreement with previous definitions is proved. A correspondence with Brown-York original formulation of the first principle of black hole thermodynamics is finally established.Comment: 29 pages with 1 figur

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

Lagrangian Symmetries of Chern-Simons Theories

This paper analyses the Noether symmetries and the corresponding conservation laws for Chern-Simons Lagrangians in dimension $d=3$. In particular, we find an expression for the superpotential of Chern-Simons gravity. As a by-product the general discussion of superpotentials for 3rd order natural and quasi-natural theories is also given.Comment: 16 pages in LaTeX, some comments and references added. to appear in Journal of Physics A: Mathematical and Genera

Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part II: BCEA Theory

The BTZ black hole solution for (2+1)-spacetime is considered as a solution of a triad-affine theory (BCEA) in which topological matter is introduced to replace the cosmological constant in the model. Conserved quantities and entropy are calculated via Noether theorem, reproducing in a geometrical and global framework earlier results found in the literature using local formalisms. Ambiguities in global definitions of conserved quantities are considered in detail. A dual and covariant Legendre transformation is performed to re-formulate BCEA theory as a purely metric (natural) theory (BCG) coupled to topological matter. No ambiguities in the definition of mass and angular momentum arise in BCG theory. Moreover, gravitational and matter contributions to conserved quantities and entropy are isolated. Finally, a comparison of BCEA and BCG theories is carried out by relying on the results obtained in both theories.Comment: PlainTEX, 20 page

Operative Outcome And Hospital Cost

AbstractIntroduction: Because of concern about increasing health care costs, we undertook a study to find patient risk factors associated with increased hospital costs and to evaluate the relationship between increased cost and in-hospital mortality and serious morbidity. Methods: More than 100 patient variables were screened in 1221 patients undergoing cardiac procedures. Simultaneously, patient hospital costs were computed from the cost-to-charge ratio. Univariate and multivariate statistics were used to explore the relationship between hospital cost and patient outcomes, including operative death, in-hospital morbidity, and length of stay. Results: The greatest costs were for 31 patients who did not survive operation ($74,466, 95$27,102 to $198,025), greater than the costs for 120 patients who had serious, nonfatal morbidity ($60,335, 95% confidence interval $28,381 to$130,897,p = 0.02) and those for 1070 patients who survived operation without complication ($31,459, 95$21,944 to $49,849, p = 0.001). Breakdown of the components of hospital costs in fatalities and in cases with nonfatal complications revealed that the greatest contributions were in anesthesia and operating room costs. Significant (by stepwise linear regression analysis) independent risks for increased hospital cost were as follows (in order of decreasing importance): (1) preoperative congestive heart failure, (2) serum creatinine level greater than 2.5 mg/dl, (3) New York state predicted mortality risk, (4), type of operation (coronary artery bypass grafting, valve, valve plus coronary artery bypass grafting, or other), (5) preoperative hematocrit, (6) need for reoperative procedure, (7) operative priority, and (8) sex. These risks were different than those for in-hospitality death or increased length of stay. Hospital cost correlated with length of stay (r = 0.63, p < 0.001), but there were many outliers at the high end of the hospital cost spectrum. Conclusions: We conclude that operative death is the most costly outcome; length of stay is an unreliable indicator of hospital cost, especially at the high end of the cost spectrum; risks of increased hospital cost are different than those for perioperative mortality or increased length of stay; and ventricular dysfunction in elderly patients undergoing urgent operations for other than coronary disease is associated with increased cost. Certain patient factors, such as preoperative anemia and congestive heart failure, are amenable to preoperative intervention to reduce costs, and a high-risk patient profile can serve as a target for cost-reduction strategies. (J Thorac Cardiovasc Surg 1998;115:593-603