Efficient digital-to-analog encoding

An important issue in analog circuit design is the problem of digital-to-analog conversion, i.e., the encoding of Boolean variables into a single analog value which contains enough information to reconstruct the values of the Boolean variables. A natural question is: what is the complexity of implementing the digital-to-analog encoding function? That question was answered by Wegener (see Inform. Processing Lett., vol.60, no.1, p.49-52, 1995), who proved matching lower and upper bounds on the size of the circuit for the encoding function. In particular, it was proven that [(3n-1)/2] 2-input arithmetic gates are necessary and sufficient for implementing the encoding function of n Boolean variables. However, the proof of the upper bound is not constructive. In this paper, we present an explicit construction of a digital-to-analog encoder that is optimal in the number of 2-input arithmetic gates. In addition, we present an efficient analog-to-digital decoding algorithm. Namely, given the encoded analog value, our decoding algorithm reconstructs the original Boolean values. Our construction is suboptimal in that it uses constants of maximum size n log n bits; the nonconstructive proof uses constants of maximum size 2n+[log n] bits

Cosmological tensor perturbations in the Randall-Sundrum model: evolution in the near-brane limit

We discuss the evolution of cosmological tensor perturbations in the RSII model. In Gaussian normal coordinates the wave equation is non-separable, so we use the near-brane limit to perform the separation and study the evolution of perturbations. Massive excitations, which may also mix, decay outside the horizon which could lead to some novel cosmological signatures.Comment: 18 pages, 1 figur

Brane-World Cosmology, Bulk Scalars and Perturbations

We investigate aspects of cosmology in brane world theories with a bulk scalar field. We concentrate on a recent model motivated from supergravity in singular spaces. After discussing the background evolution of such a brane-world, we present the evolution of the density contrast. We compare our results to those obtained in the (second) Randall-Sundrum scenario and usual 4D scalar-tensor theories.Comment: 29 pages, one figure, JHEP3-styl

Chameleon Dark Energy

Chameleons are scalar fields whose mass depends on the environment, specifically on the ambient matter density. While nearly massless in the cosmos, where the matter density is tiny, their mass is of order of an inverse millimeter on Earth, where the density is high. In this note, we review how chameleons can satisfy current experimental constraints on deviations from General Relativity (GR). Moreover, we study the cosmological evolution with a chameleon field and show the existence of an attractor solution, akin to the tracker solution in quintessence models. We discuss how chameleons can naturally drive the observed acceleration of the universeComment: 5 pages, 2 figures. To appear in the proceedings of the "Phi in the Sky" conference, 8-10 July 2004, Porto, Portugua

Time-Varying Fine-Structure Constant Requires Cosmological Constant

Webb et al. presented preliminary evidence for a time-varying fine-structure constant. We show Teller's formula for this variation to be ruled out within the Einstein-de Sitter universe, however, it is compatible with cosmologies which require a large cosmological constant.Comment: 3 pages, no figures, revtex, to be published in Mod. Phys. Lett.