Program logics for homogeneous meta-programming.

A meta-program is a program that generates or manipulates another program; in homogeneous meta-programming, a program may generate new parts of, or manipulate, itself. Meta-programming has been used extensively since macros were introduced to Lisp, yet we have little idea how formally to reason about metaprograms. This paper provides the first program logics for homogeneous metaprogramming – using a variant of MiniMLe by Davies and Pfenning as underlying meta-programming language.We show the applicability of our approach by reasoning about example meta-programs from the literature. We also demonstrate that our logics are relatively complete in the sense of Cook, enable the inductive derivation of characteristic formulae, and exactly capture the observational properties induced by the operational semantics

Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies

Heuristic arguments and numerical simulations support the Belinskii et al (BKL) claim that the approach to the singularity in generic gravitational collapse is characterized by local Mixmaster dynamics (LMD). Here, one way to identify LMD in collapsing spatially inhomogeneous cosmologies is explored. By writing the metric of one spacetime in the standard variables of another, signatures for LMD may be found. Such signatures for the dynamics of spatially homogeneous Mixmaster models in the variables of U(1)-symmetric cosmologies are reviewed. Similar constructions for U(1)-symmetric spacetimes in terms of the dynamics of generic $T^2$-symmetric spacetime are presented.Comment: 17 pages, 5 figures. Contribution to CQG Special Issue "A Spacetime Safari: Essays in Honour of Vincent Moncrief

The Singularity in Generic Gravitational Collapse Is Spacelike, Local, and Oscillatory

A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the singularity in generic gravitational collapse is spacelike, local, and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological spacetimes. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.Comment: 7 pages includes 4 figures. Uses Revtex and psfig. Received "honorable mention" in 1998 Gravity Research Foundation essay contest. Submitted to Mod. Phys. Lett.

Oscillatory approach to the singularity in vacuum T2T^2 symmetric spacetimes

A combination of qualitative analysis and numerical study indicates that vacuum $T^2$ symmetric spacetimes are, generically, oscillatory.Comment: 2 pages submitted to the Ninth Marcel Grossmann Proceedings; v2, "all known cases" changed to "various known cases" in the first paragrap

On the area of the symmetry orbits in T2T^2 symmetric spacetimes

We obtain a global existence result for the Einstein equations. We show that in the maximal Cauchy development of vacuum $T^2$ symmetric initial data with nonvanishing twist constant, except for the special case of flat Kasner initial data, the area of the $T^2$ group orbits takes on all positive values. This result shows that the areal time coordinate $R$ which covers these spacetimes runs from zero to infinity, with the singularity occurring at R=0.Comment: The appendix which appears in version 1 has a technical problem (the inequality appearing as the first stage of (52) is not necessarily true), and since the appendix is unnecessary for the proof of our results, we leave it out. version 2 -- clarifications added, version 3 -- reference correcte

Some new results on electron transport in the atmosphere

The penetration, diffusion and slowing down of electrons in a semi-infinite air medium has been studied by the Monte Carlo method. The results are applicable to the atmosphere at altitudes up to 300 km. Most of the results pertain to monoenergetic electron beams injected into the atmosphere at a height of 300 km, either vertically downwards or with a pitch-angle distribution isotropic over the downward hemisphere. Some results were also obtained for various initial pitch angles between 0 deg and 90 deg. Information has been generated concerning the following topics: (1) the backscattering of electrons from the atmosphere, expressed in terms of backscattering coefficients, angular distributions and energy spectra of reflected electrons, for incident energies T(o) between 2 keV and 2 MeV; (2) energy deposition by electrons as a function of the altitude, down to 80 km, for T(o) between 2 keV and 2 MeV; (3) the corresponding energy depostion by electron-produced bremsstrahlung, down to 30 km; (4) the evolution of the electron flux spectrum as function of the atmospheric depth, for T(o) between 2 keV and 20 keV. Energy deposition results are given for incident electron beams with exponential and power-exponential spectra

Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on T3×RT^3 \times R

A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that the singularity in generic gravitational collapse is locally oscillatory is tested numerically in vacuum, U(1) symmetric cosmological spacetimes on $T^3 \times R$. If the velocity term dominated (VTD) solution to Einstein's equations is substituted into the Hamiltonian for the full Einstein evolution equations, one term is found to grow exponentially. This generates a prediction that oscillatory behavior involving this term and another (which the VTD solution causes to decay exponentially) should be observed in the approach to the singularity. Numerical simulations strongly support this prediction.Comment: 15 pages, Revtex, includes 12 figures, psfig. High resolution versions of figures 7, 8, 9, and 11 may be obtained from anonymous ftp to ftp://vela.acs.oakland.edu/pub/berger/u1genfig

CP Violation and Arrows of Time Evolution of a Neutral KK or BB Meson from an Incoherent to a Coherent State

We study the evolution of a neutral $K$ meson prepared as an incoherent equal mixture of $K^0$ and $\bar{K^0}$. Denoting the density matrix by \rho(t) = {1/2} N(t) [\1 + \vec{\zeta}(t) \cdot \vec{\sigma} ] , the norm of the state $N(t)$ is found to decrease monotonically from one to zero, while the magnitude of the Stokes vector $|\vec{\zeta}(t)|$ increases monotonically from zero to one. This property qualifies these observables as arrows of time. Requiring monotonic behaviour of $N(t)$ for arbitrary values of $\gamma_L, \gamma_S$ and $\Delta m$ yields a bound on the CP-violating overlap $\delta = \braket{K_L}{K_S}$, which is similar to, but weaker than, the known unitarity bound. A similar requirement on $|\vec{\zeta}(t)|$ yields a new bound, $\delta^2 < {1/2} (\frac{\Delta \gamma}{\Delta m}) \sinh (\frac{3\pi}{4} \frac{\Delta \gamma}{\Delta m})$ which is particularly effective in limiting the CP-violating overlap in the $B^0$-$\bar{B^0}$ system. We obtain the Stokes parameter $\zeta_3(t)$ which shows how the average strangeness of the beam evolves from zero to $\delta$. The evolution of the Stokes vector from $|\vec{\zeta}| = 0$ to $|\vec{\zeta}| = 1$ has a resemblance to an order parameter of a system undergoing spontaneous symmetry breaking.Comment: 13 pages, 6 figures. Inserted conon "." in title; minor change in text. To appear in Physical review

Did U.S. Bank Supervisors Get Tougher During the Credit Crunch? Did They Get Easier During the Banking Boom? Did It Matter to Bank Lending?

We test three hypotheses regarding changes in supervisory toughness' and their effects on bank lending. The data provide modest support for all three hypotheses that there was an increase in toughness during the credit crunch period (1989-1992), that there was a decline in toughness during the boom period (1993-1998), and that changes in toughness, if they occurred, affected bank lending. However, all of the measured effects are small, with 1% or less of loans receiving harsher or easier classification, about 3% of banks receiving better or worse CAMEL ratings, and bank lending being changed by 1% or less of assets.