On the "renormalization" transformations induced by cycles of expansion and contraction in causal set cosmology

We study the ``renormalization group action'' induced by cycles of cosmic expansion and contraction, within the context of a family of stochastic dynamical laws for causal sets derived earlier. We find a line of fixed points corresponding to the dynamics of transitive percolation, and we prove that there exist no other fixed points and no cycles of length two or more. We also identify an extensive ``basin of attraction'' of the fixed points but find that it does not exhaust the full parameter space. Nevertheless, we conjecture that every trajectory is drawn toward the fixed point set in a suitably weakened sense.Comment: 22 pages, 1 firgure, submitted to Phys. Rev.

Payment Methods For Consumer-to-Consumer Online Transactions

Participants in online auctions use a variety of payment mechanisms, but checks and money orders still represent the most commonly used means of payment. Credit cards afford greater protection to buyers, but until recently payment by credit card was not even an option for person-to-person transactions. However, several online payment services have been established that enable individuals to make credit card payments to one another, generally with the payment service acting as an intermediary. These services are growing rapidly, mainly because of the speed and convenience that they offer. Yet relatively little attention has been paid to the risks and potential liabilities they involve for buyers and sellers. This Article compares online payment systems and similar intermediary services to traditional payment mechanisms in that context

Spam Legislation in the United States, 22 J. Marshall J. Computer & Info. L. 3 (2003)

This article examines the effect of spam legislation in the United States. It discusses state legislation and the common provisions of state spam legislation, such as disclosure and labeling requirements and opt-out provisions. It also analyzes the consequences of state anti-spam legislation. Federal legislation is analyzed, with a brief look at the CAN-SPAM Act of 2003. The article concludes that legislation has not had a big impact on spam, and the CAN-SPAM Act is not likely to change or curb spam

On the absence of homogeneous scalar unitary cellular automata

Failure to find homogeneous scalar unitary cellular automata (CA) in one dimension led to consideration of only ``approximately unitary'' CA---which motivated our recent proof of a No-go Lemma in one dimension. In this note we extend the one dimensional result to prove the absence of nontrivial homogeneous scalar unitary CA on Euclidean lattices in any dimension.Comment: 7 pages, plain TeX, 3 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages); minor changes (including title wording) in response to referee suggestions, also updated references; to appear in Phys. Lett.

Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change

We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum limit coincides with the theory obtained by quantizing 2d continuum gravity in proper-time gauge, but it disagrees with 2d gravity defined via matrix models or Liouville theory. By allowing topology change of the compact spatial slices (i.e. baby universe creation), one obtains agreement with the matrix models and Liouville theory.Comment: 30 pages, 5 figures, Latex, uses psfig.st

A numerical study of the correspondence between paths in a causal set and geodesics in the continuum

This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit.Comment: To the celebration of the 60th birthday of Rafael D. Sorki