6,832 research outputs found
Entropy for gravitational Chern-Simons terms by squashed cone method
In this paper we investigate the entropy of gravitational Chern-Simons terms
for the horizon with non-vanishing extrinsic curvatures, or the holographic
entanglement entropy for arbitrary entangling surface. In 3D we find no anomaly
of entropy appears. But the squashed cone method can not be used directly to
get the correct result. For higher dimensions the anomaly of entropy would
appear, still, we can not use the squashed cone method directly. That is
becasuse the Chern-Simons action is not gauge invariant. To get a reasonable
result we suggest two methods. One is by adding a boundary term to recover the
gauge invariance. This boundary term can be derived from the variation of the
Chern-Simons action. The other one is by using the Chern-Simons relation
. We notice that the entropy of
is a total derivative locally, i.e. . We propose
to identify with the entropy of gravitational Chern-Simons terms
. In the first method we could get the correct result for Wald
entropy in arbitrary dimension. In the second approach, in addition to Wald
entropy, we can also obtain the anomaly of entropy with non-zero extrinsic
curvatures. Our results imply that the entropy of a topological invariant, such
as the Pontryagin term and the Euler density, is a
topological invariant on the entangling surface.Comment: 19 pag
Holographic Entanglement Entropy for the Most General Higher Derivative Gravity
The holographic entanglement entropy for the most general higher derivative
gravity is investigated. We find a new type of Wald entropy, which appears on
entangling surface without the rotational symmetry and reduces to usual Wald
entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for
the most general higher derivative gravity and work it out exactly for some
squashed cones. As an important application, we derive HEE for gravitational
action with one derivative of the curvature when the extrinsic curvature
vanishes. We also study some toy models with non-zero extrinsic curvature. We
prove that our formula yields the correct universal term of entanglement
entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and
Smolkin that the logarithmic term of entanglement entropy derived from Weyl
anomaly of CFTs does not match the holographic result even if the extrinsic
curvature vanishes. We find that such mismatch comes from the `anomaly of
entropy' of the derivative of curvature. After considering such contributions
carefully, we resolve the puzzle successfully. In general, we need to fix the
splitting problem for the conical metrics in order to derive the holographic
entanglement entropy. We find that, at least for Einstein gravity, the
splitting problem can be fixed by using equations of motion. How to derive the
splittings for higher derivative gravity is a non-trivial and open question.
For simplicity, we ignore the splitting problem in this paper and find that it
does not affect our main results.Comment: 28 pages, no figures, published in JHE
The domination number and the least -eigenvalue
A vertex set of a graph is said to be a dominating set if every
vertex of is adjacent to at least a vertex in , and the
domination number (, for short) is the minimum cardinality
of all dominating sets of . For a graph, the least -eigenvalue is the
least eigenvalue of its signless Laplacian matrix. In this paper, for a
nonbipartite graph with both order and domination number , we show
that , and show that it contains a unicyclic spanning subgraph
with the same domination number . By investigating the relation between
the domination number and the least -eigenvalue of a graph, we minimize the
least -eigenvalue among all the nonbipartite graphs with given domination
number.Comment: 13 pages, 3 figure
Brainstem glucose metabolism predicts reward dependence scores in treatment-resistant major depression
BACKGROUND: It has been suggested that individual differences in temperament could be involved in the (non-)response to antidepressant (AD) treatment. However, how neurobiological processes such as brain glucose metabolism may relate to personality features in the treatment-resistant depressed (TRD) state remains largely unclear. METHODS: To examine how brainstem metabolism in the TRD state may predict Cloninger's temperament dimensions Harm Avoidance (HA), Novelty Seeking (NS), and Reward Dependence (RD), we collected (18)fluorodeoxyglucose positron emission tomography ((18)FDG PET) scans in 40 AD-free TRD patients. All participants were assessed with the Temperament and Character Inventory (TCI). We applied a multiple kernel learning (MKL) regression to predict the HA, NS, and RD from brainstem metabolic activity, the origin of respectively serotonergic, dopaminergic, and noradrenergic neurotransmitter (NT) systems. RESULTS: The MKL model was able to significantly predict RD but not HA and NS from the brainstem metabolic activity. The MKL pattern regression model identified increased metabolic activity in the pontine nuclei and locus coeruleus, the medial reticular formation, the dorsal/median raphe, and the ventral tegmental area that contributed to the predictions of RD. CONCLUSIONS: The MKL algorithm identified a likely metabolic marker in the brainstem for RD in major depression. Although (18)FDG PET does not investigate specific NT systems, the predictive value of brainstem glucose metabolism on RD scores however indicates that this temperament dimension in the TRD state could be mediated by different monoaminergic systems, all involved in higher order reward-related behavior
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