Some Remarks on Theories with Large Compact Dimensions and TeV-Scale Quantum Gravity

We comment on some implications of theories with large compactification radii and TeV-scale quantum gravity. These include the behavior of high-energy gravitational scattering cross sections and consequences for ultra-high-energy cosmic rays and neutrino scattering, the question of how to generate naturally light neutrino masses, the issue of quark-lepton unification, the equivalence principle, and the cosmological constant.Comment: 28 pages, Late

Combinatorial Representation of Generalized Fibonacci Numbers

New formulae are presented which express various generalizations of Fibonacci numbers as simple sums of binomial and multinomial coefficients. The equalities are inferred from the special properties of the representations of the integers in certain numeration systems

On the Randomness of Compressed Data

It seems reasonable to expect from a good compression method that its output should not be further compressible, because it should behave essentially like random data. We investigate this premise for a variety of known lossless compression techniques, and find that, surprisingly, there is much variability in the randomness, depending on the chosen method. Arithmetic coding seems to produce perfectly random output, whereas that of Huffman or Ziv-Lempel coding still contains many dependencies. In particular, the output of Huffman coding has already been proven to be random under certain conditions, and we present evidence here that arithmetic coding may produce an output that is identical to that of Huffman