Revisiting the Rice Theorem of Cellular Automata

A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, i.e. the infinite sequences of cell states. The limit set of the cellular automaton is the set of configurations which can be reached arbitrarily late in the evolution. In this paper, we prove that all properties of limit sets of cellular automata with binary-state cells are undecidable, except surjectivity. This is a refinement of the classical "Rice Theorem" that Kari proved on cellular automata with arbitrary state sets.Comment: 12 pages conference STACS'1

Fredholm realizations of elliptic symbols on manifolds with boundary II: fibered boundary

We consider two calculi of pseudodifferential operators on manifolds with fibered boundary: Mazzeo's edge calculus, which has as local model the operators associated to products of closed manifolds with asymptotically hyperbolic spaces, and the phi calculus of Mazzeo and the second author, which is similarly modeled on products of closed manifolds with asymptotically Euclidean spaces. We construct an adiabatic calculus of operators interpolating between them, and use this to compute the `smooth' K-theory groups of the edge calculus, determine the existence of Fredholm quantizations of elliptic symbols, and establish a families index theorem in K-theory

Business cycles, economic crises, and the poor : testing for asymmetric effects

The author examines whether output contraction associated with cyclical output fluctuations and economic crises have an asymmetric effect on poverty. He identifies four potential sources of asymmetry: expectations and cofident factors, credit rationing at the firm level (induced by either adeverse selection problems or negative shocks to net worth), borrowing constraints at the household level, and the"labor hoarding"hypothesis. He also identifies some testable implications of these alternative explanations. The author then proposes a vector autoregression technique (involving the detrended components of real output, the unemployment rate, real wages, and the poverty rate) to test whether the initial cyclical position of the economy, and the size of the initial drop in the output gap in a downturn, matter in assessing the extent to which output shocks affect poverty. He applies the technique to Brazil, using annual data for 1981-99. The results indicate that poverty responds asymmetrically to output shocks, showing less sensitivity when the economy is initially in a downturn.Economic Theory&Research,Environmental Economics&Policies,Labor Policies,Health Economics&Finance,Public Health Promotion,Environmental Economics&Policies,Economic Theory&Research,Health Economics&Finance,Achieving Shared Growth,Health Monitoring&Evaluation

Trapping effects on the vibration-inversion-rotation motions of an ammonia molecule encapsulated in C60_{60} fullerene molecule

The infrared bar-spectrum of a single ammonia molecule encapsulated in nano-cage C$_{60}$ fullerene molecule is modelled using the site inclusion model successfully applied to analyze spectra of CO$_2$ isotopologues isolated in rare gas matrix. Calculations show that NH$_3$ can rotate freely on a sphere of radius 0.184 $\text{\AA}$ around the site centre of the nano-cage and spin freely about its C$_3$ symmetry axis. In the static field inside the cage degenerate $\nu_3$ and $\nu_4$ vibrational modes are blue shifted and split. When dynamic coupling with translational motion is considered, the spectral signature of the $\nu_2$ mode is modified with a higher hindering barrier (2451 cm$^{-1}$), an effective reduced mass (6.569 g.mol$^{-1}$) and a longer tunneling time (55594 ps) for the fundamental level compared to gas-phase values (2047 cm$^{-1}$), (2.563 g.mol$^{-1}$) and (20.85 ps). As a result this mode is red shifted. Moreover, simulation shows that the changes in the bar-spectrum of the latter mode can be used to probe the temperature of the surrounding media in which fullerene is observed

Van't Hoff law for temperature dependent Langmuir constants in clathrate hydrate nanocavities

This work gives a van't Hoff law expression of Langmuir constants of different species for determining their occupancy in the nanocavities of clathrate hydrates. The van't Hoff law's parameters are derived from a fit with Langmuir constants calculated using a pairwise site-site interaction potential to model the anisotropic potential environment in the cavities, as a function of temperature. The parameters can be used for calculating clathrates compositions. Results are given for nineteen gas species trapped in the small and large cavities of structure types I and II [1]. The accuracy of this approach is based on a comparison with available experimental data for ethane and cyclo- propane clathrate hydrates. The numerical method applied in this work, was recently validated from a comparison with the spherical cell method based on analytical considerations [1]Comment: 2 figure

Computing the Two-Sided Kolmogorov-Smirnov Distribution

We propose an algorithm to compute the cumulative distribution function of the two-sided Kolmogorov-Smirnov test statistic D_n and its complementary distribution in a fast and reliable way. Different approximations are used in different regions of n, x. Java and C programs are available.