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A formal specification of primary-backup is presented. We then prove lower bounds on the degree of replication, failover time, and worst-case response time to client requests assuming different failure models. Finally, we outline primary-backup protocols and indicate which of our lower bounds are tight.
The application of a sector-based stability theory approach to the formulation of useful uncertainty descriptions for linear, time-invariant, multivariable systems is explored. A review of basic sector properties and sector-based approach are presented first. The sector-based approach is then applied to several general forms of parameter uncertainty to investigate its advantages and limitations. The results indicate that the sector uncertainty bound can be used effectively to evaluate the impact of parameter uncertainties on the frequency response of the design model. Inherent conservatism is a potential limitation of the sector-based approach, especially for highly dependent uncertain parameters. In addition, the representation of the system dynamics can affect the amount of conservatism reflected in the sector bound. Careful application of the model can help to reduce this conservatism, however, and the solution approach has some degrees of freedom that may be further exploited to reduce the conservatism.
It is demonstrated that a complete-active-space self-consistent-field (CASSCF) (2p)/MRCI + Q (multireference configuration interaction with a Davidson correction) description in a (13s8p6d 4f2g)/((5s4p3d 2f1g) atomic natural orbits (ANO) basis set supplemented with diffuse functions provides a quantitative description of the six lowest states of O2. The calculated potentials are within 0.05 eV (1.2 kilocal/mol) of accurate experimental results. The importance of substantially expanding the primitive basis set has been investigated, and it is demonstrated that such expansions yield insignificant improvement in the spectroscopic constants. Potential energy curves have also been reported for the weakly bound states of O2. The 5Pi(g) state is estimated to have a D(e) of 0.16 +/- 0.03 eV. The upper bound of D(e) is found to be sufficiently large that the importance of this state as a precursor for the formation of O2 (b 1Sigma(t)(+)) and O(1S) should be reconsidered.
The problem of robust stability in linear systems with parametric uncertainties is considered. A method is developed to determine bounds on uncertain parameters in the state-space model of the system, so that stability is preserved. Both continuous- and discrete-time systems are considered. Unlike previous results, the stability bounds are derived in terms of actual parameters instead of their absolute values, and consequently the stable region in the parameter space is not necessarily symmetric with respect to the origin. Furthermore, the uncertain parameters do not have to be linearly independent to each other.
The linear programming spectral overbounding and factorization (LPSOF) algorithm, an algorithm for finding a minimum phase transfer function of specified order whose magnitude tightly overbounds a specified nonparametric function of frequency, is introduced. This method has direct application to transforming nonparametric uncertainty bounds (available from system identification experiments) into parametric representations required for modern robust control design software (i.e., a minimum-phase transfer function multiplied by a norm-bounded perturbation).
An error bound is derived for a reliability model approximation method. The approximation method is appropriate for the semi-Markov models of reconfigurable systems that are designed to achieve extremely high reliability. The semi-Markov models of these system are complex, and a significant amount of their complexity arises from the detailed descriptions of the reconfiguration processes. The reliability model approximation method consists of replacing a detailed description of a reconfiguration process with the probabilities of the possible outcomes of the reconfiguration process. These probabilities are included in the model as instantaneous jumps from the fault-occurrence state. Since little time is spent in the reconfiguration states, instantaneous jumps are a close approximation to the original model. This approximation procedure is shown to produce an overestimation for the probability of system failure, and an error bound is derived for this overestimation.
In this paper three models of parallel speedup are studied. They are fixed-size speedup, fixed-time speedup and memory-bounded speedup. The latter two consider the relationship between speedup and problem scalability. Two sets of speedup formulations are derived for these three models. One set considers uneven workload allocation and communication overhead and gives more accurate estimation. Another set considers a simplified case and provides a clear picture on the impact of the sequential portion of an application on the possible performance gain from parallel processing. The simplified fixed-size speedup is Amdahl's law. The simplified fixed-time speedup is Gustafson's scaled speedup. The simplified memory-bounded speedup contains both Amdahl's law and Gustafson's scaled speedup as special cases. This study leads to a better understanding of parallel processing.
The quantification of model uncertainty is becoming increasingly important as robust control is an important tool for control system design and analysis. This paper presents an algorithm that effectively characterizes the model uncertainty in terms of parametric and nonparametric uncertainties. The algorithm utilizes the frequency domain model error which is estimated from the spectra of output error and input data. The parametric uncertainty is represented as an interval transfer function while the nonparametric uncertainty is bounded by a designed error bound transfer function. Both discrete and continuous systems are discussed in this paper. The algorithm is applied to the Mini-Mast example, and the detail analysis is given.
Thermodynamic models have been formulated to predict lower and upper bounds for the mass of pressurant gas required to pressurize a cryogenic tank and then expel liquid from the tank. Limiting conditions are based on either thermal equilibrium or zero energy exchange between the pressurant gas and initial tank contents. The models are independent of gravity level and allow specification of autogenous or non-condensible pressurants. Partial liquid fill levels may be specified for initial and final conditions. Model predictions are shown to successfully bound results from limited normal-gravity tests with condensable and non-condensable pressurant gases. Representative maximum collapse factor maps are presented for liquid hydrogen to show the effects of initial and final fill level on the range of pressurant gas requirements. Maximum collapse factors occur for partial expulsions with large final liquid fill fractions.
The Griesmer bound is a classical technique (developed in 1960) for estimating the minimum length n required for a binary linear code with a given dimension k and minimum distance d. In this article, a unified derivation of the Griesmer bound and two new variations on it are presented. The first variation deals with linear codes which contain the all-ones vector; such codes are quite common and are useful in practice because of their 'transparent' properties. The second variation deals with codes that are constrained to contain a word of weight greater than or equal to M. In both cases these constraints (the all-ones word or a word of high weight) can increase the minimum length of a code with given k and d.
This work addresses the problem of assigning confidence intervals to estimated photometry data obtained from astronomical observations. The proposed solution is to estimate the Cramer-Rao bound, which is an analytical expression that describes the minimum obtainable mean square error associated with a given estimate of a parameter. This Letter presents a compact and simple form for the bound associated with a linear estimator such as a Wiener filter estimator. A prescription for estimating the variance associated with each element in a restored object was developed using an analytical model for observed data corrupted by either Poisson or Gaussian noise. Both one- and two-dimensional examples are presented.
Maximum likelihood decoding of long block codes is not feasable due to large complexity. Some classes of codes are shown to be decomposable into multilevel concatenated codes (MLCC). For these codes, multistage decoding provides good trade-off between performance and complexity. In this paper, we derive an upper bound on the probability of block error for MLCC. We use this bound to evaluate difference in performance for different decompositions of some codes. Examples given show that a significant reduction in complexity can be achieved when increasing number of stages of decoding. Resulting performance degradation varies for different decompositions. A guideline is given for finding good m-level decompositions.
This project extends the study of the structure of wall-bounded flows using the topological properties of eddying motions as developed by Chong et al. (1990), Soria et al. (1992, 1994), and as recently extended by Blackburn et al. (1996) and Chacin et al. (1996). In these works, regions of flow which are focal in nature are identified by being enclosed by an isosurface of a positive small value of the discriminant of the velocity gradient tensor. These regions resemble the attached vortex loops suggested first by Theodorsen (1955). Such loops are incorporated in the attached eddy model versions of Perry & Chong (1982), Perry et al. (1986), and Perry & Marusic (1995), which are extensions of a model first formulated by Townsend (1976). The DNS data of wall bounded flows studied here are from the zero pressure gradient flow of Spalart (1988) and the boundary layer with separation and reattachment of Na & Moin (1996). The flow structures are examined from the viewpoint of the attached eddy hypothesis.
When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.
A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information. In the present paper, we develop an algorithm based on identities which determine the jumps of a 2(pi)-periodic bounded not-too-highly oscillating function by the partial sums of its differentiated Fourier series. The algorithm enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. We study the accuracy of approximation and establish asymptotic expansions for the approximations of a 27(pi)-periodic piecewise smooth function with one discontinuity. By an appropriate linear combination, obtained via derivatives of different order, we significantly improve the accuracy. Next, we use Richardson's extrapolation method to enhance the accuracy even more. For a function with multiple discontinuities we establish simple formulae which "eliminate" all discontinuities of the function but one. Then we treat the function as if it had one singularity following the method described above.
We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.
General expressions (with potential applications in several areas of geophysical fluid dynamics) are derived for all three components of the contribution made by the geostrophic part of the pressure field associated with flow in a rotating gravitating fluid to the topographic torque exerted by the fluid on a rigid impermeable bounding surface of any shape. When applied to the Earth's liquid metallic core, which is bounded by nearly spherical surfaces and can be divided into two main regions, the "torosphere" and "polosphere," the expressions reduce to formulae given previously by the author, thereby providing further support for his work and that of others on the role of topographic coupling at the core-mantle boundary in the excitation by core motions of Earth rotation fluctuations on decadal time scales. They also show that recent criticisms of that work are vitiated by mathematical and physical errors. Contrary to these criticisms, the author's scheme for exploiting Earth rotation and other geophysical data (either real or simulated in computer models) in quantitative studies of the topography of the core-mantle boundary (CMB) by intercomparing various models of (a) motions in the core based on geomagnetic secular variation data and (b) CMB topography based on seismological and gravity data has a sound theoretical basis. The practical scope of the scheme is of course limited by the accuracy of real data, but this is a matter for investigation, not a priori assessment.
We improve, using a larger set of observations including Voyager 2 Neptune flyby data, previous bounds on the amount of dark matter (DM) trapped in a spherically symmetric distribution about the Sun. We bound DM by noting that such a distribution would increase the effective mass of the Sun as seen by the outer planets and by finding the uncertainty in that effective mass for Uranus and Neptune in fits to the JPL developmental ephemeris residuals, including optical data and those two planets' Voyager 2 flybys. We extend our previous procedure by fitting more parameters of the developmental ephamerides. In addition, we present here the values for Pioneer 10, Pioneer 11, Voyager 1, and Voyager 2 Jupiter-ranging normal points (and incorporate these data as well). Our principal result is to limit DM in spherically symmetric distributions in orbit about the Sun interior to Neptune's orbit to less than Earth mass and interior to Uranus's orbit to about 1/6 of Earth's mass.