Thinking Together: The Value of Discussion in the Five Year Old\u27s Classroom

Illustrates a kindergarten classroom where the teacher places a high value upon questions - child or adult generated. Discussion is the centerpiece of the program

Toll-managed lane pioneers: Lessons from five US states

Toll-managed lanes have become an increasingly popular technique among transportation policymakers for managing congestion on existing highways and, in some cases, financing the construction of new lanes in congested urban corridors. Although growing in popularity, the adoption of these facilities is concentrated in five states: Texas, California, Colorado, Minnesota, and Florida. This paper examines the adoption and utilization of toll-managed lanes in these pioneer states. Using archival, case-based research, our analysis suggests that the adoption of toll-managed lanes was driven by a combination of factors, including rapid population growth, near or above average growth in vehicle miles traveled (VMT), and insufficient gas tax funding for transportation investments. Implementation was also generally similar across states but some of the pioneers delegated the management of their toll-managed lane programs to special regional highway authorities while others used state highway agencies

Remarks on Resonant Scalars in the AdS/CFT Correspondence

The special properties of scalars having a mass such that the two possible dimensions of the dual scalar respect the unitarity and the Breitenlohner-Freedman bounds and their ratio is integral (``resonant scalars'') are studied in the AdS/CFT correspondence. The role of logarithmic branches in the gravity theory is related to the existence of a trace anomaly and to a marginal deformation in the Conformal Field Theory. The existence of asymptotic charges for the conformal group in the gravity theory is interpreted in terms of the properties of the corresponding CFT.Comment: 16 pages, 1 figur

Universal Features of Holographic Anomalies

We study the mechanism by which gravitational actions reproduce the trace anomalies of the holographically related conformal field theories. Two universal features emerge: a) the ratios of type B trace anomalies in any even dimension are independent of the gravitational action, being uniquely determined by the underlying algebraic structure b) the normalization of the type A and the overall normalization of the type B anomalies are given by action dependent expressions with the dimension dependence completely fixed.Comment: 17 pages, harvma

General solutions of the Wess-Zumino consistency condition for the Weyl anomalies

The general solutions of the Wess-Zumino consistency condition for the conformal (or Weyl, or trace) anomalies are derived. The solutions are obtained, in arbitrary dimensions, by explicitly computing the cohomology of the corresponding Becchi-Rouet-Stora-Tyutin differential in the space of integrated local functions at ghost number unity. This provides a purely algebraic, regularization-independent classification of the Weyl anomalies in arbitrary dimensions. The so-called type-A anomaly is shown to satisfy a non-trivial descent of equations, similarly to the non-Abelian chiral anomaly in Yang-Mills theory.Comment: 9 pages. RevTeX fil

A classification of local Weyl invariants in D=8

Following a purely algebraic procedure, we provide an exhaustive classification of local Weyl-invariant scalar densities in dimension D=8.Comment: LaTeX, 19 pages, typos corrected, one reference adde

Dynamics of Asymptotic Diffeomorphisms in (2+1)-Dimensional Gravity

In asymptotically anti-de Sitter gravity, diffeomorphisms that change the conformal boundary data can be promoted to genuine physical degrees of freedom. I show that in 2+1 dimensions, the dynamics of these degrees of freedom is described by a Liouville action, with the correct central charge to reproduce the entropy of the BTZ black hole.Comment: 8 pages, LaTeX; v2: slightly expanded discussion of implications, more references; v3: more explicit comparison to Chern-Simons approach and discussion of role of constraints; v4: added discussion of relationships to and differences with earlier work, new and corrected reference

Violation of Energy Bounds in Designer Gravity

We continue our study of the stability of designer gravity theories, where one considers anti-de Sitter gravity coupled to certain tachyonic scalars with boundary conditions defined by a smooth function W. It has recently been argued there is a lower bound on the conserved energy in terms of the global minimum of W, if the scalar potential arises from a superpotential P and the scalar reaches an extremum of P at infinity. We show, however, there are superpotentials for which these bounds do not hold.Comment: 16 pages, 4 figures, v2: discussion of vacuum decay included, typos corrected, reference adde

Diffeomorphisms and Holographic Anomalies

Using the relation between diffeomorphisms in the bulk and Weyl transformations on the boundary we study the Weyl transformation properties of the bulk metric on shell and of the boundary action. We obtain a universal formula for one of the classes of trace anomalies in any even dimension in terms of the parameters of the gravity action.Comment: 12 pages, harvma

Counterterms and dual holographic anomalies in CS gravity

The holographic Weyl anomaly associated to Chern-Simons gravity in 2n+1 dimensions is proportional to the Euler term in 2n dimensions, with no contributions from the Weyl tensor. We compute the holographic energy-momentum tensor associated to Chern-Simons gravity directly from the action, in an arbitrary odd-dimensional spacetime. We show, in particular, that the counterterms rendering the action finite contain only terms of the Lovelock type.Comment: 10 pages, no figure