35,211 research outputs found
Quantum Yang-Mills gravity in flat space-time and effective curved space-time for motions of classical objects
Yang-Mills gravity with translational gauge group T(4) in flat space-time
implies a simple self-coupling of gravitons and a truly conserved
energy-momentum tensor. Its consistency with experiments crucially depends on
an interesting property that an `effective Riemannian metric tensor' emerges in
and only in the geometric-optics limit of the photon and particle wave
equations. We obtain Feynman rules for a coupled graviton-fermion system,
including a general graviton propagator with two gauge parameters and the
interaction of ghost particles. The equation of motion of macroscopic objects,
as an N-body system, is demonstrated as the geometric-optics limit of the
fermion wave equation. We discuss a relativistic Hamilton-Jacobi equation with
an `effective Riemann metric tensor' for the classical particles.Comment: 20 pages, to be published in "The European Physical Journal -
Plus"(2011). The final publication is available at http://www.epj.or
Clustering in Hilbert space of a quantum optimization problem
The solution space of many classical optimization problems breaks up into
clusters which are extensively distant from one another in the Hamming metric.
Here, we show that an analogous quantum clustering phenomenon takes place in
the ground state subspace of a certain quantum optimization problem. This
involves extending the notion of clustering to Hilbert space, where the
classical Hamming distance is not immediately useful. Quantum clusters
correspond to macroscopically distinct subspaces of the full quantum ground
state space which grow with the system size. We explicitly demonstrate that
such clusters arise in the solution space of random quantum satisfiability
(3-QSAT) at its satisfiability transition. We estimate both the number of these
clusters and their internal entropy. The former are given by the number of
hardcore dimer coverings of the core of the interaction graph, while the latter
is related to the underconstrained degrees of freedom not touched by the
dimers. We additionally provide new numerical evidence suggesting that the
3-QSAT satisfiability transition may coincide with the product satisfiability
transition, which would imply the absence of an intermediate entangled
satisfiable phase.Comment: 11 pages, 6 figure
A VLSI single chip (255,223) Reed-Solomon encoder with interleaver
A single-chip implementation of a Reed-Solomon encoder with interleaving capability is described. The code used was adapted by the CCSDS (Consulative Committee on Space Data Systems). It forms the outer code of the NASA standard concatenated coding system which includes a convolutional inner code of rate 1/2 and constraint length 7. The architecture, leading to this single VLSI chip design, makes use of a bit-serial finite field multiplication algorithm due to E.R. Berlekamp
A simplified procedure for correcting both errors and erasures of a Reed-Solomon code using the Euclidean algorithm
It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial and the error evaluator polynomial in Berlekamp's key equation needed to decode a Reed-Solomon (RS) code. A simplified procedure is developed and proved to correct erasures as well as errors by replacing the initial condition of the Euclidean algorithm by the erasure locator polynomial and the Forney syndrome polynomial. By this means, the errata locator polynomial and the errata evaluator polynomial can be obtained, simultaneously and simply, by the Euclidean algorithm only. With this improved technique the complexity of time domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches. As a consequence, decoders for correcting both errors and erasures of RS codes can be made more modular, regular, simple, and naturally suitable for both VLSI and software implementation. An example illustrating this modified decoding procedure is given for a (15, 9) RS code
Approximating random quantum optimization problems
We report a cluster of results regarding the difficulty of finding
approximate ground states to typical instances of the quantum satisfiability
problem -QSAT on large random graphs. As an approximation strategy, we
optimize the solution space over `classical' product states, which in turn
introduces a novel autonomous classical optimization problem, PSAT, over a
space of continuous degrees of freedom rather than discrete bits. Our central
results are: (i) The derivation of a set of bounds and approximations in
various limits of the problem, several of which we believe may be amenable to a
rigorous treatment. (ii) A demonstration that an approximation based on a
greedy algorithm borrowed from the study of frustrated magnetism performs well
over a wide range in parameter space, and its performance reflects structure of
the solution space of random -QSAT. Simulated annealing exhibits
metastability in similar `hard' regions of parameter space. (iii) A
generalization of belief propagation algorithms introduced for classical
problems to the case of continuous spins. This yields both approximate
solutions, as well as insights into the free energy `landscape' of the
approximation problem, including a so-called dynamical transition near the
satisfiability threshold. Taken together, these results allow us to elucidate
the phase diagram of random -QSAT in a two-dimensional
energy-density--clause-density space.Comment: 14 pages, 9 figure
How well do CMIP5 climate simulations replicate historical trends and patterns of meteorological droughts?
Assessing the uncertainties and understanding the deficiencies of climate models are fundamental to developing adaptation strategies. The objective of this study is to understand how well Coupled Model Intercomparison-Phase 5 (CMIP5) climate model simulations replicate ground-based observations of continental drought areas and their trends. The CMIP5 multimodel ensemble encompasses the Climatic Research Unit (CRU) ground-based observations of area under drought at all time steps. However, most model members overestimate the areas under extreme drought, particularly in the Southern Hemisphere (SH). Furthermore, the results show that the time series of observations and CMIP5 simulations of areas under drought exhibit more variability in the SH than in the Northern Hemisphere (NH). The trend analysis of areas under drought reveals that the observational data exhibit a significant positive trend at the significance level of 0.05 over all land areas. The observed trend is reproduced by about three-fourths of the CMIP5 models when considering total land areas in drought. While models are generally consistent with observations at a global (or hemispheric) scale, most models do not agree with observed regional drying and wetting trends. Over many regions, at most 40% of the CMIP5 models are in agreement with the trends of CRU observations. The drying/wetting trends calculated using the 3 months Standardized Precipitation Index (SPI) values show better agreement with the corresponding CRU values than with the observed annual mean precipitation rates. Pixel-scale evaluation of CMIP5 models indicates that no single model demonstrates an overall superior performance relative to the other models
A comparison of VLSI architectures for time and transform domain decoding of Reed-Solomon codes
It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial needed to decode a Reed-Solomon (RS) code. It is shown that this algorithm can be used for both time and transform domain decoding by replacing its initial conditions with the Forney syndromes and the erasure locator polynomial. By this means both the errata locator polynomial and the errate evaluator polynomial can be obtained with the Euclidean algorithm. With these ideas, both time and transform domain Reed-Solomon decoders for correcting errors and erasures are simplified and compared. As a consequence, the architectures of Reed-Solomon decoders for correcting both errors and erasures can be made more modular, regular, simple, and naturally suitable for VLSI implementation
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