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This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check (LDPC) codes and variations of repeat-accumulate codes). The transmission of the code ensembles is assumed to take place over a binary erasure channel, and the bounds refer to the asymptotic case where we let the block length tend to infinity. The simplicity of the bounds derived in this paper stems from the fact that they are easily evaluated and are expressed in terms of some basic parameters of the ensemble which include the fraction of degree-2 variable nodes, the target bit erasure probability, and the gap between the channel capacity and the design rate of the ensemble. This paper demonstrates that the number of iterations which is required for successful message-passing decoding scales at least like the inverse of the gap (in rate) to capacity, provided that the fraction of degree-2 variable nodes of these turbo-like ensembles does not vanish (hence, the number of iterations becomes unbounded as the gap to capacity vanishes). [ABSTRACT FROM AUTHOR]

Coarse-graining (CG) techniques have recently attracted great interest for providing descriptions at a mesoscopic level of resolution that preserve fluid thermodynamic and transport behaviors with a reduced number of degrees of freedom and hence less computational effort. One fundamental question arises: how well and to what extent can a 'bottom-up' developed mesoscale model recover the physical properties of a molecular scale system? To answer this question, we explore systematically the properties of a CG model that is developed to represent an intermediate mesoscale model between the atomistic and continuum scales. This CG model aims to reduce the computational cost relative to a full atomistic simulation, and we assess to what extent it is possible to preserve both the thermodynamic and transport properties of an underlying reference all-atom Lennard-Jones (LJ) system. In this paper, only the thermodynamic properties are considered in detail. The transport properties will be examined in subsequent work. To coarse-grain, we first use the iterative Boltzmann inversion (IBI) to determine a CG potential for a (1-[lowercase_phi_synonym])N mesoscale particle system, where [lowercase_phi_synonym] is the degree of coarse-graining, so as to reproduce the radial distribution function (RDF) of an N atomic particle system. Even though the uniqueness theorem guarantees a one to one relationship between the RDF and an effective pairwise potential, we find that RDFs are insensitive to the long-range part of the IBI-determined potentials, which provides some significant flexibility in further matching other properties. We then propose a reformulation of IBI as a robust minimization procedure that enables simultaneous matching of the RDF and the fluid pressure. We find that this new method mainly changes the attractive tail region of the CG potentials, and it improves the isothermal compressibility relative to pure IBI. We also find that there are optimal interaction cutoff lengths for the CG system, as a function of [lowercase_phi_synonym], that are required to attain an adequate potential while maintaining computational speedup. To demonstrate the universality of the method, we test a range of state points for the LJ liquid as well as several LJ chain fluids. [ABSTRACT FROM AUTHOR]

The movement of the hydraulically driven six degrees of freedom (6-DOF) parallel platform is driven by six sets of valve-controlled asymmetrical cylinders (VCACs), so the precision of the platform is mainly determined by the control precision of the VCACs. Unfortunately, the asymmetrical movement of the VCACs caused by its asymmetrical structure can significantly compromise control precision because of this asymmetry, and more fundamentally, with the inherent non-linearity of hydraulic systems as well as complicated load variations, it is very difficult to achieve ideal control precision with traditional PID control. In the present study, the working principle and characteristics of a VCAC were analysed, with particular focus on the asymmetry problem. In order to improve the precision of both VCAC control and 6-DOF parallel platform movement, a PD-type iterative learning control (ILC) method is presented, and applied to a hydraulically driven 6-DOF parallel platform. Experiments on both the single VCAC system and the parallel platform were developed to verify the validity and effectiveness of this control method. The theoretical analysis and testing results, compared with those for the conventional PID control, proved that the proposed PD-type ILC method can acquire high precision on the 6-DOF parallel platform without the need to build a mathematical model or obtain accurate loading conditions. [ABSTRACT FROM PUBLISHER]