Energy in higher-derivative gravity via topological regularization

Indexación: Scopus.We give a novel definition of gravitational energy for an arbitrary theory of gravity including quadratic-curvature corrections to Einstein's equations. We focus on the theory in four dimensions, in the presence of a negative cosmological constant, and with asymptotically anti-de Sitter (AdS) boundary conditions. As a first example, we compute the gravitational energy and angular momentum of Schwarzschild-AdS black holes, for which we obtain results consistent with previous computations performed using different methods. However, our method is qualitatively different due to the fact that it is intrinsically nonlinear. It relies on the idea of adding to the gravity action topological invariant terms which suffice to regularize the Noether charges and render the variational problem well-posed. This is an idea that has been previously considered in the case of second-order theories, such as general relativity and which, as shown here, extends to higher-derivative theories. Besides black holes, we consider other solutions such as gravitational waves in AdS, for which we also find results that are in agreement. This enables us to investigate the consistency of this approach in the non-Einstein sector of the theory. © 2018 authors. Published by the American Physical Society.https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.04404

Isostaticity and the solidification of semiflexible polymer melts

Using molecular dynamics simulations of a tangent-soft-sphere bead-spring polymer model, we examine the degree to which semiflexible polymer melts solidify at isostaticity. Flexible and stiff chains crystallize when they are isostatic as defined by appropriate degree-of-freedom-counting arguments. Semiflexible chains also solidify when isostatic if a generalized isostaticity criterion that accounts for the slow freezing out of configurational freedom as chain stiffness increases is employed. The dependence of the average coordination number at solidification $Z(T_s)$ on chains' characteristic ratio $C_\infty$ has the same functional form [$Z \simeq a - b\ln(C_\infty)$] as the dependence of the average coordination number at jamming $Z(\phi_J)$ on $C_\infty$ in athermal systems, suggesting that jamming-related phenomena play a significant role in thermal polymer solidification

Spectral Bounds for the Connectivity of Regular Graphs with Given Order

The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to connectivity attributes such as the vertex- and edge-connectivity, isoperimetric number, and characteristic path length. In this paper, we present two upper bounds for the second-largest eigenvalues of regular graphs and multigraphs of a given order which guarantee a desired vertex- or edge-connectivity. The given bounds are in terms of the order and degree of the graphs, and hold with equality for infinite families of graphs. These results answer a question of Mohar.Comment: 24 page

Teacher Perceptions of the American School Counselor Association’s National Model in an Urban Setting

The development of the ASCA’s National Standards and Model has helped define the profession and provided a framework for school counselors to implement in designing a program. Despite recent clarity in the school counseling profession, barriers still exist, especially in urban settings. As collaborators, teachers perceptions were measured in regards to urban school counselors implementing ASCA’s Model and its components (Elements/ Themes). Overall, results showed that teachers were in favor of the ASCA National Model and its components. Teacher’s gender and number of years teaching did not significantly influence responses to survey questions. Despite high perceptions of the model, more research needs to be conducted in urban schools to determine if this model is practical and feasible

Effects of Bulk Viscosity on Cosmological Evolution

The effect of bulk viscisity on the evolution of the homogeneous and isotropic cosmological models is considered. Solutions are found, with a barotropic equation of state, and a viscosity coefficient that is proportional to a power of the energy density of the universe. For flat space, power law expansions, related to extended inflation are found as well as exponential solutions, related to old inflation; also a solution with expansion that is an exponential of an exponential of the time is found.Comment: 8 pages, latex, no figure

On the G-protein-coupled receptor heteromers and their allosteric receptor-receptor interactions in the central nervous system: focus on their role in pain modulation

The modulatory role of allosteric receptor-receptor interactions in the pain pathways of the Central Nervous System and the peripheral nociceptors has become of increasing interest. As integrators of nociceptive and antinociceptive wiring and volume transmission signals, with a major role for the opioid receptor heteromers, they likely have an important role in the pain circuits and may be involved in acupuncture. The delta opioid receptor (DOR) exerts an antagonistic allosteric influence on the mu opioid receptor (MOR) function in a MOR-DOR heteromer. This heteromer contributes to morphine-induced tolerance and dependence, since it becomes abundant and develops a reduced G-protein-coupling with reduced signaling mainly operating via beta-arrestin 2 upon chronic morphine treatment. A DOR antagonist causes a return of the Gi/o binding and coupling to the heteromer and the biological actions of morphine. The gender- and ovarian steroid-dependent recruitment of spinal cord MOR/kappa opioid receptor (KOR) heterodimers enhances antinociceptive functions and if impaired could contribute to chronic pain states in women. MOR1D heterodimerizes with gastrin-releasing peptide receptor (GRPR) in the spinal cord, mediating morphine induced itch. Other mechanism for the antinociceptive actions of acupuncture along meridians may be that it enhances the cross-desensitization of the TRPA1 (chemical nociceptor)-TRPV1 (capsaicin receptor) heteromeric channel complexes within the nociceptor terminals located along these meridians. Selective ionotropic cannabinoids may also produce cross-desensitization of the TRPA1-TRPV1 heteromeric nociceptor channels by being negative allosteric modulators of these channels leading to antinociception and antihyperalgesia