Punctured Trellis-Coded Modulation

In classic trellis-coded modulation (TCM) signal constellations of twice the cardinality are applied when compared to an uncoded transmission enabling transmission of one bit of redundancy per PAM-symbol, i.e., rates of $\frac{K}{K+1}$ when $2^{K+1}$ denotes the cardinality of the signal constellation. In order to support different rates, multi-dimensional (i.e., $\mathcal{D}$-dimensional) constellations had been proposed by means of combining subsequent one- or two-dimensional modulation steps, resulting in TCM-schemes with $\frac{1}{\mathcal{D}}$ bit redundancy per real dimension. In contrast, in this paper we propose to perform rate adjustment for TCM by means of puncturing the convolutional code (CC) on which a TCM-scheme is based on. It is shown, that due to the nontrivial mapping of the output symbols of the CC to signal points in the case of puncturing, a modification of the corresponding Viterbi-decoder algorithm and an optimization of the CC and the puncturing scheme are necessary.Comment: 5 pages, 10 figures, submitted to IEEE International Symposium on Information Theory 2013 (ISIT

- AN EVOLUTIONARY MODEL OF BERTRAND OLIGOPOLY

We analyze the long-run outcome of markets in which boundedly rational firms with a decreasingreturns to scale technology compete in prices. The behavior of these firms is based on limitation ofsuccess and experimentation. In this framework, we introduce a new approach to model boundedlyrational behavior, based on the idea of behavioral principles, i.e. formal descriptions. Even with thesimplest ones, the result is that the prices announced are a strict refinement of the set of Nashequilibria. With more sophisticated behavioral principles, the long-run outcome corresponds to theconcept of central prices (wich are also Nash equilibria) introduced here. This is a robust andclear-cut prediction wich, under quadratic costs and arbitrary demand, essentially coincides with theWalrasian equilibrium.evolution, mutation, imitation

Estimates of Comet Fragment Masses from Impact Crater Chains on Callisto and Ganymede

Chains of impact craters, or catenae, have been identified in Voyager images of Callisto and Ganymede. Although these resemble in some respects secondary crater chains, the source craters and basins for the catenae cannot be identified. The best explanation is a phenomenon similar to that displayed by former comet Shoemaker-Levy 9; tidal (or other) breakup close to Jupiter followed by gradual orbital separation of the fragments and collision with a Galilean satellite on the outbound leg of the trajectory. Because the trajectories must pass close to Jupiter, this constrains the impact geometry (velocity and impact angle) of the individual fragments. For the dominant classes of impactors, short period Jupiter-family comets and asteroids, velocities at Callisto and Ganymede are dominated by Jovian gravity and a satellite's orbital motion, and are insensitive to the pre-fragmentation heliocentric velocity; velocities are insensitive to satellite gravity for all impactor classes. Complex crater shapes on Callisto and Ganymede are determined from Voyager images and Schmidt-Holsapple scaling is used to back out individual fragment masses. We find that comet fragment radii are generally less than about 500 m (for ice densities) but can be larger. These estimates can be compared with those for the Shoemaker-Levy 9 impactors

Transport properties of a superconducting single-electron transistor coupled to a nanomechanical oscillator

We investigate a superconducting single-electron transistor capacitively coupled to a nanomechanical oscillator and focus on the double Josephson quasiparticle resonance. The existence of two coherent Cooper pair tunneling events is shown to lead to pronounced backaction effects. Measuring the current and the shot noise provides a direct way of gaining information on the state of the oscillator. In addition to an analytical discussion of the linear-response regime, we discuss and compare results of higher-order approximation schemes and a fully numerical solution. We find that cooling of the mechanical resonator is possible, and that there are driven and bistable oscillator states at low couplings. Finally, we also discuss the frequency dependence of the charge noise and the current noise of the superconducting single electron transistor.Comment: 19 pages, 11 figures, published in PR

Triton's surface age and impactor population revisited in light of Kuiper Belt fluxes: Evidence for small Kuiper Belt objects and recent geological activity

Neptune's largest satellite, Triton, is one of the most fascinating and enigmatic bodies in the solar system. Among its numerous interesting traits, Triton appears to have far fewer craters than would be expected if its surface was primordial. Here we combine the best available crater count data for Triton with improved estimates of impact rates by including the Kuiper Belt as a source of impactors. We find that the population of impactors creating the smallest observed craters on Triton must be sub-km in scale, and that this small-impactor population can be best fit by a differential power-law size index near -3. Such results provide interesting, indirect probes of the unseen small body population of the Kuiper Belt. Based on the modern, Kuiper Belt and Oort Cloud impactor flux estimates, we also recalculate estimated ages for several regions of Triton's surface imaged by Voyager 2, and find that Triton was probably active on a time scale no greater than 0.1-0.3 Gyr ago (indicating Triton was still active after some 90% to 98% of the age of the solar system), and perhaps even more recently. The time-averaged volumetric resurfacing rate on Triton implied by these results, 0.01 km$^3$ yr$^{-1}$ or more, is likely second only to Io and Europa in the outer solar system, and is within an order of magnitude of estimates for Venus and for the Earth's intraplate zones. This finding indicates that Triton likely remains a highly geologically active world at present, some 4.5 Gyr after its formation. We briefly speculate on how such a situation might obtain.Comment: 14 pages (TeX), plus 2 postscript figures Stern & McKinnon, 2000, AJ, in pres

3-Dimensional Core-Collapse

In this paper, we present the results of 3-dimensional collapse simulations of rotating stars for a range of stellar progenitors. We find that for the fastest spinning stars, rotation does indeed modify the convection above the proto-neutron star, but it is not fast enough to cause core fragmentation. Similarly, although strong magnetic fields can be produced once the proto-neutron star cools and contracts, the proto-neutron star is not spinning fast enough to generate strong magnetic fields quickly after collapse and, for our simulations, magnetic fields will not dominate the supernova explosion mechanism. Even so, the resulting pulsars for our fastest rotating models may emit enough energy to dominate the total explosion energy of the supernova. However, more recent stellar models predict rotation rates that are much too slow to affect the explosion, but these models are not sophisticated enough to determine whether the most recent, or past, stellar rotation rates are most likely. Thus, we must rely upon observational constraints to determine the true rotation rates of stellar cores just before collapse. We conclude with a discussion of the possible constraints on stellar rotation which we can derive from core-collapse supernovae.Comment: 34 pages (5 of 17 figures missing), For full paper, goto http://qso.lanl.gov/~clf/papers/rot.ps.gz accepted by Ap